Ma bibliothèque mathématique, et
connexes, au 8 janvier 2019 (par une mise à jour annuelle), principalement
de des livres et des articles, mais aussi des lettres,
brochures, critiques, brevets, thèses, énigmes, énigmes, expositions
catalogues, conférences, vidéos, notes, rapports, articles de journaux, critiques, interviews,
décès et problèmes familiaux.
Ceci est une collection personnelle de références avec des notes et des commentaires à
Ma propre recherche mathématique s’applique particulièrement aux tessellations et aux
Aspects de type Escher, comme cela a tendance à l'être, et cela peut être utile
d'autres chercheurs. Les dates entre parenthèses ont la date d'obtention de la publication. Parfois
on cite un livre qui n’est pas en ma possession, mais bien le désir de le mentionner
pour un certain nombre de raisons, même si cela est indiqué dans le texte. À l'occasion
Un livre référencé qui est trop avancé pour que je sois inutile, en général
à partir d'une bibliographie. Un exemple typique serait de Carrelages et motifs
par Branko Grünbaum et G. C. Shephard. C'est juste avoir "vu et noté"
donc je peux me reposer facilement qu'il n'y a rien d'autre qui aurait pu être éteint
Cela a été commencé en 2006 et se poursuit jusqu'à aujourd'hui. Notez que
Le texte peut être considéré comme une œuvre perpétuelle en raison de sa nature, de plusieurs livres et articles, et d’autres qui sont mis au jour. La longueur et la profondeur de
Chaque entrée dépend en grande partie de la signification du livre / article, même si je suis
Pas toujours cohérent dans ce désir. Toutes les entrées n'ont pas de commentaires, en raison de
contraintes de temps. Parfois, vous pouvez taper et imprimer en tant que
le résultat inévitable d'un travail d'une telle longueur et profondeur. De plus, même si je le fais
s'efforcer d'être cohérent, ce n'est pas toujours possible; J'ai en fait d'autres
choses à assister!
Quelques explications sur ce qui pourrait autrement apparaître comme un texte peu clair:
1. On peut voir de nombreuses références aux tuiles du Caire et se référer à la mienne
Intérêt particulier pour cette tuile.
2. Certaines annonces commencent par & # 39; partir d'une vente de bibliothèque & # 39;. Généralement avec d'autres
Si les acheteurs sont présents, il est préférable de conserver le livre et d'examiner en détail
plus tard dans la vente, ou plus tard à la maison. Habituellement, les livres ont un prix égal à
sont négligeables, souvent des sous, ou pas plus d’une livre. Tel parent
De petites sommes d’argent sont donc toujours là, donnant ainsi des livres
intérêt possible (dans n'importe quel sujet) que je ne pourrais normalement pas payer
plein ou même moitié prix pour. La somme en jeu est incohérente et peut
donc écrit à ce sujet s'avère être inutile.
3. Certaines entrées commencent par "hasard" ou "achat spéculatif". cette
se réfère à un livre vu dans un sens temporel, par une vente de voiture ou autre
en tant que vente, disponible uniquement sur l'option unique ponctuelle. Enregistrer pour un
Un intérêt évident, typique d'un livre d'intérêt possible, est assez simple
Pas le temps de regarder chaque côté d'un long livre pour le thème
intérêts, et dont le prix est généralement différent, une livre sterling
ou en dessous, et plutôt que de perdre l'occasion, il est considéré comme prudent
Pour obtenir le livre, la somme en jeu est insignifiante et peut donc être écrite
si cela s'avère inutile.
4. Certaines références à des énigmes peuvent autrement paraître floues dans un cas.
contexte mathématique, mais qu'est-ce qu'un puzzle si ce n'est une tessellation? ici
Mais ce sont des questions historiques ou des mathématiques de toute nature
qui les sous-tend.
5. Certaines annonces ont des détails de base tels que l'auteur, souvent pris
de Wikipedia. C’est généralement là où l’auteur peut être moins familier,
Et je veux connaître un peu le contexte.
Abas, Syed Jan et Amer Shaker Salman (avec préface de
Ahmed Mousafa (calligraphie arabe) et Sir Michael Atiyah). Symétries de
Motifs géométriques islamiques. World Scientific 1995. (12 décembre 2009)
Reliure petit format, 396 pp.
À partir de la page 140 sur, seulement par cartes. Un scientifique, mais toujours populaire
compte de tuiles islamiques. J'aime ce livre plus que la plupart des autres
thème, qui manque généralement rigueur. Les extraits d'intérêt incluent: Khatem
Suleimani (étoile et croix à huit branches, sceau de Soloman) p. 14-15. Ceci est également connu comme "Souffle de la
Compassionate, à Chorbaci. Cependant, cela semble être un titre "non officiel";
sur recherche En utilisant le terme Abass, il n’ya presque rien et ce qu’il est juste fait référence à abbas Une autre merveille est la légende de description de & # 39; Soloman & # 39;
Seal; Il s'agit généralement d'un pentagramme d'hexagramme, plutôt que de celui-ci.
étoile à huit branches. Feuille de figue (feuille d'érable) p.102. a une bonne bibliographie avec
quelques références non données ailleurs. Pas de tuiles du Caire.
Wikipedia fournit: Le sceau
de Salomon (ou anneau de Salomon; arabe: خاتم سليمانKhātam Sulaymān)
Abbott, David (éditeur général). La biographique
Dictionnaire de chercheurs. mathématiciens. Blond International 1985 (22 juin
Compte populaire d'un
séries scientifiques (comprend astronomes, ingénieurs et inventeurs), avec ici
mathématiques. A un glossaire et un index. Nombreuses entrées sur la géométrie. Cela étant dit,
La plupart des listes vont au-delà de mon domaine d’intérêt direct et de compréhension, mais cela
Tout le monde fait toujours plaisir à lire.
Abbott, P. géométrie. (Apprendre ailleurs
Vous-même des livres) The English Universities Press Ltd. 1962 Première impression en 1948
(19 juillet 1992) et Hodder et Stoughton.
1981 (26 juillet 1992)
Texte de géométrie générique typique
Le livre d'aujourd'hui, l'un des nombreux que j'ai; simplement on aurait suffi. ils
L'objet de ce livre était de pouvoir rechercher des motifs géométriques.
construction au fur et à mesure, mais je ne pense pas l’avoir utilisée dans
de toute façon.
Abbott. algèbre (20 janvier 1987)
Abbott, P. et C. E. Kerridge. Certificat national
mathématiques. Volumes 1 et 2 Technique
Série universitaire. ils
English Universities Press Ltd 1961 (19 juillet 1992, 26 juillet 1992, 21 juin 1992)
Manuel, un peu avancé. de
pas d'utilisation pratique
Aczel, Amir D. La dernière théorie de Fermat. Déverrouiller le secret d'un vieil homme
Problème mathématique. Penguin Books 1997 (16 juillet 2007)
Compte populaire de l'historique
missions; beaucoup de graduations et de bons fils.
Adams, D. M. inorganique
Solides: Introduction aux concepts de la chimie structurale à l'état solide.
Wiley-Blackwell, 1974. (Premier cas, ou du moins enregistré, le 24 septembre 1987, à l'université
Une étude plus petite, dans laquelle les études de cristal sont partagés
avec d'autres livres de la même nature.
Mathématiques. L'histoire des chiffres, des symboles et des pièces. Golden Press Nouveau
York, 1958. (3 septembre 1995)
Juvénile, 56 pp. 8-11 ans
région. Pas de tessellation. Etrange, pas structuré du tout, être sans
introduction et contenu. Larges images mathématiques d'une large gamme.
Notez qu'Adler était également actif en mathématiques et était l'un des
écrivain fructueux. De Wikipedia:
Un livre Adler a écrit pour les adultes
en 1958, Les nouvelles mathématiques,
était important dans la réforme du curriculum "New Math" et l'a conduit
apparitions fréquentes à des réunions de formation partout en Amérique du Nord.
—-. Groupes dans les nouvelles mathématiques. Livres Dobson
Ltd. Première publication au Royaume-Uni en 1968 (21 février 1998).
Sans intérêt! D'une bibliothèque
vente, sur la possibilité d'intérêt possible. Dit d'être un intermédiaire
niveau, pas techniquemais pas trop simple. Pas de tessellation.
Agostini. Franco. Jeux visuels. Guild Publishing de
événement avec Macdonald & Co. 1988. (5 février 1994)
Moins texte Escher pp. 80-81, Foss, Le paradis et j'ai gagné images. Bizarrement, le Le paradis et j'ai gagné l'impression est recadrée de manière asymétrique!
—-. Jeux mathématiques et logiques. Macdonald (sic)
& Co. 1983 (27 juillet 1992).
Escher En hausse et
descendantpage 34 Mobius Strip IIpage 74, pas de texte, juste des légendes.
Ahrens, W. Entretiens mathématiques et
Jeux et loisirs, Leipzig 1901 (Téléchargé à partir des archives Internet du 21 avril
une référence dans Bradley (et MacMahon). Récréation mathématique générale, dans le style
par Rouse Ball. Comme Rouse Ball, très peu sur les carreaux, à peine mentionné.
Ainsley, Robert. Vous bluffer en maths. Ravette Limitée
1988. (9 juin 2002)
format de poche, 62 pp. Un guide de Bluffer en tant que tel peut être vu dans de nombreux autres
sujets et biographies de mathématiques
couvert, court, avec un blanc sec. Comme vous pouvez l'imaginer, un compte populaire,
Bien que le diagramme soit gratuit. Pas de tessellation / Escher. D'intérêt p. 39 à Coriolis
effet, sur la faille (?) de la germination de l’eau dans un hémisphère différent. Ainsley
prétendre que cela est dû à la forme de la baignade. Pour enquêter. À l'heure du café
Albarn, Keith et Jenny Miall
Smith. Schéma. pensée instrument.
Thames et Hudson, 1977 (26 juillet 2015)
un non-sens, dans la "meilleure" tradition de Keith Critchlow. illisible
enregistrer pour parcourir de chaque côté. Une ruse préférée ici est de citer connue
chercheur / mathématiciens pour donner au livre une crédibilité perçue. petit
aspects de la tessellation, dans la perception, pp. 40, 43 et le design islamique, art.
Alexanderson, Christopher, Sara Ishikawa et Murray
Silverstein. Un langage de modèle. villes,
Secteur du bâtiment. Centre pour la structure environnementale, Berklely, Californie.
Volume 2 d'un ensemble de 3 volts (PDF) Oxford University Press, 1977 (12 septembre
A partir d'une référence de architecture place Henn, par rapport à une référence de déformation de parquet découverte.
Au cours de l'enquête, j'ai trouvé le livre au format PDF. Un volume plus lourd de 1 171 pages! beaucoup
A ma grande contrariété, ayant vu tout le livre, je n’ai pas pu trouver
référence! Si c'est un parquet
référence de déformation, il ne peut être que très mineur. Cependant, alors que recherche, J'ai trouvé
une grande partie du livre le plus intéressant au sens général, et idéalement, je
aimerait lire ceci (idéalement comme un livre, au lieu d'un pdf).
Cependant, la longueur me met (au fil du temps), pratiquement
le matériel semble être! De plus, j’ai regardé plus en arrière-plan de
Alexanderson, par qui précédemment Je n'étais pas au courant. J'étais tellement il était encore
living, avait un site web (avec des vignettes in situ) et plusieurs livres à son nom,
comme je vois son intérêt pour les dessins en soi. Son nom a alors commencé à apparaître
dans des papiers à carreaux. Probablement maintenant, complètement fondé, je trouverai des références à lui dans
Amiraslan, I. Tessellations azerbaïdjanaises, 2006 WANTED
Anderson, Paul et Deborah Curry. Mondes imaginatifs. Histoires de découvertes scientifiques. Ariel Books
British Broadcasting Corporation, 1985. (28 août 1996, mais vu beaucoup plus tôt,
en avril 1989)
Divers essais sur scientifique
découverte d'éminents scientifiques, dont Roger Penrose. d'intérêt général
dans l’ensemble, avec un aspect en mosaïque du chapitre 9 (par Deborah Curry), Beyond
Space-Time, p. 161-180, à Penrose, avec un petit intérêt en mosaïque; Penrose
les poulets page 177, et l'empreinte d'Escher Foss,
179, avec une discussion populaire sur les carreaux de Penrose.
Andrew, H. E. Laye, rédacteur en chef. Reader's Digest Manuel d'artisanat. Reader's Digest Association Limited, 1980. Première vue, ou du moins
enregistré le 2 décembre 1987 à la bibliothèque Scartho.
Bien qu'il n'y ait pas de livre dessus
math, inclus dans cette entrée car il a un pavage, de chevauchement
cercles, de moindre nature, page 97, que j’ai brièvement étudiés (une seule feuille).
En tant que tel, non pertinent, à la fois en mathématiques et en étude de celles-ci. 432 pages.
Angel, Henry. Voler et solide
géométrie. William Collins, Sons & Co., limitée, 1885 (21 juin 1992)
Livre de géométrie typique de
jour. Commencez facilement à partir des premiers principes, puis discutez plus techniquement
questions. La seule tuile est à la page 26, un problème lors de la copie d'une tuile donnée
(carré et octogone). Je semble avoir recueilli de nombreuses instances de ce type dans
début des années 1990; Certains correspondent vraiment à mes besoins.
Anon. Brique et béton. Par les éditeurs (auteur) à
Livres Time-Life. 1984. Le 21 décembre 1987, bibliothèque de Scartho
Bien qu'il n'y ait pas de livre dessus
mathématiques, inclus sur cette note car il a carreaux de brique, page 76, dont
J'ai étudié les cartes (une seule feuille), avec des ajouts proto Escher-like, 21, 23 décembre 1987 et 5 janvier. qui
Alors de toute façon.
Anon. Design et design.
Editeur non fourni
une référence sur une feuille du 17 janvier 1989. Mais quand vous cherchez l'exact
titre, il n'y a pas de livre avec ce nom qui soit en corrélation avec le temps d'étude.
Peut-être était-ce un titre capital? Quoi qu'il en soit, l'étude était sans importance, juste une trace d'un puzzle de contour.
Anonyme. Formes de serpent magique.
Corgi 1981 (14 juillet 1991)
Livre de poche de petite taille, sur 96
pp, mis en évidence à l’apogée de cet engouement pour les spin-offs Rubik Cube. Un court
Introduction d'une seule page, suivie du champ d'image du représentant
formes que Magic Snake peut former. Aucune instruction en tant que telle, sauf pour
Anonyme. Dessin technique. Letts (22 mars 1987)
une référence pour les premières études de mathématiques, 1986-1987.
Anonyme. Géométrie lettre O (23 mars 1987)
une référence pour les premières études de mathématiques, 1986-1987.
Anonyme. Les nouvelles mathématiques
référence pour les premières études de mathématiques, 1986-1987 (17 décembre 1986).
Anonyme. Longman Maths 1 (13 et 18 février 1986) et 2 (12 février 1987)
D'une référence aux mathématiques précoces
Anonyme. Mathématiques pour 16 ans (1 janvier 1987) de Bennet?
Anonyme. Plan pratique et géométrie solide
—-. ils Social ou mille et un plaisirs de plus. 1858 New York,
Dick & Fitzgerald (téléchargé depuis Internet le 10 juin 2014). 375 pages
Le site de Stegmann. Le mieux décrit une série de "jeux de société", tels que l'acteur et
tours de magie, populaire dans la journée. Lumière mathématique avec deux petits chapitres
sur les jeux mathématiques: jeux au coin du feu pour amuser l'hiver pp 274-84, Puzzle
et paradoxes curieux 286-300. Réponses aux énigmes et aux paradoxes 301-318. ces
contient des dissections géométriques lâches, mais rien de spécial.
—-. 'Des tours à portée de main
et oeil & # 39; Courrier de l'UNESCO Volume 19, n ° 5 (1966), p.
L’année habituelle, 1964 (Locher, Schattsneider), est fausse, c’est-à-dire
1966, tel que fourni par tous les auteurs où cela est cité; tout copier d'un
un autre, probablement de? Locher a raison)
Une partie de la déception, pas de texte dans la note, avec seulement deux des
Les images d'Escher utilisées, belvédère et
Childcraft Volume 13. Livre mondial Childcraft International, Inc. 1979 (21
polyèdres, pas de tessellation.
—-. Étrangetés. en
Mots, images et chiffres. Association du Reader's Digest Limitée 1975.
(Juillet 1996 et 20 août 2003? L’année est semi-lisible). Deux copies
Petit format & # 39; Livret & # 39; 48
pages. Tirages Escher et essais mineurs, p. 25-28: belvédère, Fosset
Ascendant et descendant
Voir aussi un compagnon postérieur
le livret de 1988.
—-. Projet d'enseignement des mathématiques Nuffield. 1971.
(22 août 2004)
Une série de packages "cartes de travail":
Zone (contient Cairo
pentagone, sans référence au Caire),
Égalité 1, Égalité 2, Nombre de modèles, Topologie, Nombre de modèles.
—-. L'Encyclopédie Universelle de Mathématiques. avec
une préface de James A. Newman. Pan Books Ltd, 1976. Publié pour la première fois en Grande-Bretagne.
Royaume-Uni 1964 par George Allen & Unwin Ltd. Traduit et personnalisé à partir de
original allemand Meyers Rechenduden,
publié en 1960 par le Bibliographisches Institut à Mannheim (1er avril 1993)
Grand petit format
Livre de poche, à 715 pp! Sur le plan académique, même si l’on dit, chez les éditeurs
remarque (p. 6), qui "… signifiait pour l'homme de la rue … & # 39; est une façon
au-delà du public indiqué. Formule biaisée. Pas de tessellation. Rien qui puisse
est dit être récréatif. Les polyèdres étoiles de Kepler, pages 270-271. De juste
utilisation de référence possible. Je n'ai pas l'intention de relire.
—-. Le monde de la forme et du nombre. Marshall
Système d'apprentissage Cavendish. Première publication en 1970 (6 février 1994).
Jeunesse avancée. populaire
compte sur la forme et le nombre, avec grand intérêt. Pas de tessellation cependant!
—-. Artfile Patterns. Phaidon Press Limited 1990
(14 mai 2005).
Juste des motifs, pas de texte.
et Generalife. (11 juillet 2004)
On dirait que le guide touristique (je suis
En outre, un autre livre, portant le même titre) n’a pas de date, peut-être
côté déchiré …
—-. Mathématiques à l'école primaire. les conseils scolaires
Syllabus N ° 1. HMSO
une carte d'ottagones d'intérêt.
—-. Éléments visuels
3. Clip Art Mark et Pattern. Colomb
Livres c 1989. (2 avril 1994)
Strictement un livre de modèle,
plutôt que des mathématiques. Livre 3 de 10 d'une série "d'éléments visuels"
prémisse. En tant que tel, de très peu d'intérêt; Le carrelage n’est pas un tissu, c’est
Subumé parmi les modèles de papier peint.
—-. Illusions visuelles.
Reader's Digest 1988. (20 août 2003? L'année est lisible)
Brochure encombrement réduit, 48
pages. Escher pp. 20-31, Jour et nuit.
Dans une large mesure, une histoire d'illusions existantes. Voir aussi un compagnon plus tard,
Apsley, Brenda (conçu par). Color Patterns: Fun patterns. Editions internationales du monde
Restreint. 1993 (1er avril 1993).
Adolescent. Voir aussi un
livre associé, de même nature. Un livre de coloriage pour enfants, presque d'un
niveau de cinq ans! En regardant à nouveau les deux livres, je ne comprends pas pourquoi je suis
atteint ceux-ci, et à plein prix! Les cartes sont comme prévu pour
leur public, sans aucun défi. Cela dit, c'est un graphique occasionnel
(tessellation) d’intérêt – voir page 29 ici, et p Motifs d'image ci-dessous. Je ne peux que croire que je pensais ne pas l'avoir
vu ces carreaux, puis ces livres peuvent également être relativement faibles
—-. (Conçu par). teinture
Pattern: motifs d'image. World International Publishing Limited. 1993 (1
Armstrong, Tim. Créer des modèles en mouvement. Comment faire de l'optique
Des illusions à vous. Publications Tarquin. 1982 (16 février 1991 (utilisé)
et 18 février 2007 (intact)
Livre de format carré, 56
pp. Fournit des instructions pour composer des illusions géométriques acétate superposer avec une série de grilles, conçues pour être découpées et expérimentées.
Le texte est léger. Pas avancé en aucune façon. Pas de tessellation. Dans quelle mesure ces
les idées sont originales avec Armstrong n'est pas précisé. aussi voir son deuxième livre, La perception des couleurs.
étudié en 1991, mais pas dans une large mesure. De faible intérêt
plus tôt, mais peut-être moins maintenant (2018) et pendant longtemps.
Perception. Une approche pratique de la théorie des couleurs. Publications Tarquin
1991 (30 avril 1994)
Pas strictement mathématique, bien que
a occasionnellement des croisements.
? Harpe P. De La. Quelques Problèmes Non Résolus et Géométrie Plane. L'enseignement mathématique,
t 35 (1989), p. 227-243 (en français)
Caire Pavage page 232, probablement tiré de George Martin
travail, étant donné qu'il s'agit de la même configuration "inhabituelle".
c fin 2011?
Arnold, Arnold. Les gagnants … et d'autres perdants dans la guerre et la paix.
Livres Paladin Grafton. 1989 (12 mars 1999)
En tant que tel, c'est en jeu
la théorie, et est d'une lecture lourde, écrasante de texte, 431 p., avec mathématique
aspects de l'annexe. Probablement atteint, à un prix de transaction, sur
chance pour plus tard utilité. Cependant, il n'est pas apparu! Je doute beaucoup
Si j'ai même commencé à lire ceci, ne me souviens pas de tout le livre. Encore plus aujourd'hui, moi
simplement ne pas avoir le temps de lire. Je ne me souviens pas de références à Arnold
ou ce livre. Cependant, il s’agit en réalité d’un véritable lien de jeu de société; il a conçu
Logo Parker Brothers.
Arnold (6 février 1921 – 20 janvier 2012) était un écrivain, un jeu
designer et cybernétique, plus connu pour la renommée de ses proches
et les femmes plus tard dans la vie. son
La première et unique épouse légale, Eve Arnold, était connue pour la photographie. son
Les autres partenaires, avec lesquels il ne s'est jamais marié, étaient l'auteur Gail E. Haley. Arnold
Les deux beaux-frères étaient Theodor Gaster et Peter Drucker.
… Arnold suivit son aîné
sœur des États-Unis où il a travaillé comme écrivain et bande dessinée. il
a été rédigé dans l'armée américaine en 1941 … Arnold était également un succès et
bien connu designer publicitaire et commercial, et a créé le célèbre Parker
Le logo tourbillonnant de Brother, utilisé pour la première fois en 1964. Il a créé et conçu de nombreux
jeux éducatifs et éducatifs innovants pour les principaux concepteurs de jeux
1960. Il a également réalisé des pochettes de disques classiques pour EPIC
Records dans les années 1950.(
… Dans les années 1980 et 1990, Arnold a publié plusieurs livres, mais plus jamais
eu une carrière financièrement réussie. Il est retourné à Petersfield en 1998,
où sa santé a rapidement décliné. Il est décédé en 2012 des suites de complications
de la septicémie et la pneumonie.
Arnold, George et
Frank Cahill. ils Propre livre du magicien ou
Tout l'art de briller. 1862. New York, Dick & Fitzgerald, 18 ans
Street, London (téléchargé à partir d'Internet le 18 juin 2014)
Recommandé sur le site Web de Rob Stegmann, bien qu'il soit en réalité magique, a beaucoup
mathématiques récréatives; voir en particulier la section sur les aspects géométriques:
& Astuces curieuses en géométrie & # 39; pp. 256-266, & # 39; Curious & Fun Puzzle & # 39;
Ashcroft, Mike. Cahier GCSE de mathématiques 0,1988. (15 octobre
Tessellations page 130, à peine
mérite d'être mentionné. Manuels scolaires.
Ashurst, F. Gareth. Fondateurs des mathématiques modernes. Frederick
Muller Ltd; Première édition 1982. 128 pages. Petit format. D'abord regardé
Bibliothèque Nunsthorpe, bien que l’auteur et la date n’aient pas été enregistrés, mais doivent
a été en 1987. L’auteur a ensuite été découvert par des recherches sur Internet.
Cartes apparemment étudiées,
probablement d’une seule feuille, probablement, car la discussion aurait été d’une
nature plus avancée, avec laquelle je me souviens des biographies de mathématiciens avancés.
Cependant, certaines pages étaient plus accessibles que d’autres, avec un espace saturé
courbes, dont j'ai copié les diagrammes et le texte textuel. Mais c'est tout
rien d'original ici de ma part.
Le livre a longtemps été supprimé
du magasin de la bibliothèque, et qui bien que disponible à un disponible
prix, £ 7.79, je n’en ai pas besoin d’urgence, et je ne travaille pas activement
Ceci, peu importe à quel point il serait idéal autrement.
Augarde, Tony. Oxford
Guide des jeux de mots. Oxford
University Press 1984.
(26 mai 1996)
Pas strictement mathématique, bien que
liés d'une manière, avec le jeu de mots. 26 chapitres
Mesiriac. Problèmes plaisan et
Delectables pour voir la police pour les nombres. 1612. A. Labosne Paris 1884
(téléchargé depuis Internet le 5 mai 2015)
De référence dans MacMahon. Comme ce titre l'indique,
c'est entièrement sur les chiffres; pas de carrelage que ce soit.
Bain, Iain. Knotwork celtique.
Constable London 1991. (3 juin 1993)
Baker, Lyndon et al. l'art
Maskinmønsterbok. Leapfrogs Ltd. 1990.
Ball, Johnny. Pensez à un nombre. Radiodiffusion britannique
Corporation 1979. (16 février 1995) (savon
bulles page 59)
—-. Johnny Ball est
Boîte de réflexion. Puffin Books, 1982 (17 janvier 1998)
Pour les enfants Une collection de
BBC TV enfants série de Pensez à un certain nombre et aux retombées, pensez à
Encore une fois & # 39 ;, & # 39; Pensez en arrière et # 39; Think This Way & # 39; avec le matériel rassemblé comme un
livre. En tant que tel, cela ne semble pas être original ici, avec Martin
Gardner crédité comme l'inspiration principale. De plus intérêt, relativement
On parle, pages 70 à 71, sur des carreaux avec les carrés.
—-. Merveilles au-delà
Grand. Une brève histoire de tout mathématiquement. Bloomsbury Sigma,
2017, bibliothèque de Grimsby (7 octobre 2017)
Compte populaire. Avoir beaucoup
friandises intéressantes, quelque chose de nouveau pour moi. Mais la longueur du livre (480
pages) contrecarre une lecture revue, puis certaines pages ne sont que
mousse. Le Golden Ratio, p. 50-51, constitue un aspect particulièrement intéressant.
où il me donne une nouvelle explication. Kepler pp. 306-314 insert de plaque harmonica
mundi page 313, Tessellation, pages 457 à 458,
bien qu'un traitement léger. Escher, pages 428-429, à nouveau facilement. chaussée
et tuile Alhambra sur la plaque de couleur. Nécessite idéalement une lecture plus calme
une fois de plus.
Ball, Phillip. Concevoir un monde moléculaire. chimie
à la frontière. Princeton
University Press 1994 (19
Chapitre 4, pp. 111-141 a
beaucoup sur les quasi-cristaux et les carreaux de penrose. La page d'Escher et un texte plus petit 128-129.
Ball, W.W. Rouse et Coxeter, H.S.M. mathématique
Loisirs et Essais. (treizième édition). Dover Publications, Inc.1987. (30 avril 1994)
pavage, pp. 105-107 seulement.
Banchoff, Thomas F. Au-delà de la troisième dimension. géométrie
Infographie et dimensions supérieures. (Distribué) W.H. Freeman et
Société 1990. (30 avril 1994)
Un peu difficile à décrire,
le livre se compose de concepts avancés en géométrie à un niveau largement populaire,
fortement illustré. En gros, il est de dimensions supérieures ou inférieures à
bois. Pas de tessellation.
Barber, Frederick et al. "Carrelage d'avion". faculté
Module Avancées en mathématiques, Lexington, Mass., 1989 LOOK FOR. (Référence
Barnard, D. St P. Le découvrir. Pan Books Ltd 1973 (20
Barr, Stephen. Expérience en
topologie. John Murray, Londres.
1965 (9 juillet 1994)
Dans une large mesure
compte populaire, même si je ne poursuis pas activement le sujet. La plupart des notes est
Chapitre 3, La bande la plus courte de Moebuis, p. 32-39, et Chapitre 7, Peinture de cartes & # 39;
pp. 88-97. L'idée de Moebius est si simple, et pourtant je n'y avais jamais pensé! quelques-uns
Le matériel est pris des autres.
Barratt, Krome. logique
Et le design dans l'art, la science et les mathématiques. The Herbert Press 1989. Premier
édition 1980. (24 avril 2016)
D'abord vu et étudié
1993, à la bibliothèque de l'école d'art de Grimsby. Décidé de devenir actif plus tard
(2016) sur le désir de revoir l'étude que j'avais précédemment réalisée. À réception,
la mémoire du livre s'est estompée. Je ne sais pas trop quoi faire à ce sujet. Je suis
Pas si sûr de la connaissance en mathématiques de Barrett, un concepteur. Il semble être un
compilation d’autres sources, presque sans originalité. le livre
conducteur, dans un sujet présenté, avant encore un autre, et un autre …. Je
bref, sa portée est trop ambitieuse; Il n'y a rien en profondeur ni en substance.
La bibliographie est au moins exhaustive. Carrelage mineur, non
conséquence p 47, 53, 66-67, 70-71, 196-197. Il a d'autres aspects mineurs de celui-ci
intérêt. En tant que tel, je n'ai pas l'intention "d'étudier" cela à nouveau.
Barrow, John D. Pi dans le ciel. Compter, penser et
Être. Penguin Books 1992 (22 juillet 2001).
Livre de poche de petite taille, 317 pp,
d'intérêt limité semi-populaire, pas facilement décrit, principalement "mathématiquement
réflexions philosophiques & # 39; Barrow peut être mieux connu comme un astronome. paroles
lourd, avec seulement des cartes occasionnelles. Pas de tessellation, Escher. Les chiffres de
différents pays, page 44, Hypothèses de lutte contre les incendies, pages 227-234. Dans l'ensemble, c'est
"Intéressant", mais le temps que cela prend maintenant (2018) pour lire ceci serait
disproportionné à tous les gains je doute.
Bok. Millésime 2005 (24 janvier 2015)
Avoir des trucs courts avec
signifie carreaux du Caire page 16, mais sans attribution, et Penrose
tuiles. Fait aussi moins référence à Escher, pp.130-131, avec son empreinte Spirales Sphère, fait référence aux loxodromes.
Beard, R. S. (Colonel) modèles
dans l'espace. Creative Publications Inc. 1973.
Sur des côtés géométriques, sur neuf
chapitres: polygones, polygones Tessellés, motifs de polyèdres, section dorée,
Nombres de Fibonacci et dessins associés, coniques et courbes, spirales, triangles
relations, triangles primitifs, divers. Beaucoup de formules données,
bien que la prémisse soit un livre dirigé par un graphique. Malgré un chapitre sur "Tesselated
Les polygones, 23-42, ne concernent pas vraiment les mosaïques, mais plutôt des "patchs",
et des constructions généralement géométriques. Le travail sur les mosaïques est pris
de, ou a été inspiré par. Article sur la barbe Scripta Mathematicae, avec le même titre, qui est reproduit dans
livre. Beaucoup de formules sont trop compliquées pour moi, mais ça reste
Les graphiques sont principalement disponibles. Cependant, le livre flatte en grande partie pour tromper.
Beer, Arthur et Peter Beer (rédacteurs). Rester dans
Astronomie. Quatre cents ans de conférences à l'honneur
Johannes Kepler. Vol.18. Pergamon Press. 1975. (c 2001)
grande collection d'articles (sur 1034 pages!) issus de la conférence.
Peut-être que quelques mosaïques surprenantes, et dans une certaine mesure, des polyèdres sont
Pas vraiment discuté. Au lieu de cela, c'est vraiment plus de son travail astronomique. chapitre
11 est décrit comme "Kepler, mathématicien et physicien". D'intérêt ici
est l'essai de Coxeter "Kepler and Mathematics", p. 661-670. Voir aussi le chapitre 14, p.
861-876 & Idées cristallographiques de Kepler et son entonnoir & # 39; Les Six Coins
Flocon de neige de I. I. Shafranovskii, qui touche le paquet circulaire et est
Begelman, Mitchell et Martin Rees. L'attraction fatale de la gravité: des trous noirs dans l'univers
Cambridge University Press (Google Books, 16 juin 2015)
Utilisation d'Escher Limite circulaire, Anges et diables pp. 80-81. (**)
Bekkering, Betsy et Geert Bekkering. Pièce par pièce: histoire du puzzle aux Pays-Bas.
1988 (en néerlandais) Pièce par pièce: une histoire sur le casse-tête de
Pays-Bas (20 mars 2016) Traduction imprimée le 27 janvier 2017
Atteint en ce qui concerne
intérêts dans les blagues groupées, bien que Bekkering me le dise dans un courrier
2014 qu'il n'y a rien dans ce domaine. A des détails sur la base de
Simplex pp. 57-58, et également à la page 30. Bien que
Il n'y a rien ici sur le gémissement en soi, c'est toujours intéressant
pour plus de détails sur l’histoire des puzzles néerlandais.
Bekkering, Geert. Spass
et patience: l'histoire des énigmes en Allemagne. (En allemand) traduit:
Amusement et patience: l'histoire de
puzzles en Allemagne. Husum. 2004 (20 mars 2016) Traduction écrite 27
Atteint en ce qui concerne
intérêts dans les puzzles de cluster, avec une connexion Bekkering. Encore une fois, comme ci-dessus,
Il n'y a rien d'intérêt direct. Cependant, c’est vraiment un intérêt périphérique,
de ce que j'ai supposé peut se produire, donc achat spéculatif. P. 56 a Heye
Profi puzzle, qui utilise une adaptation de la position de runman d'Escher
(sans crédit en retard), et après une enquête plus poussée peut fonctionner
a été utilisé sur de nombreux autres casse-tête de la société. Pp. 56-57 gi a
Histoire de l'entreprise. Pp. 66, 68, 90, 92 sont intéressants à montrer un
& # 39; Wavy Square & # 39; tessellation coupe, de 1914.
E. T. Reine des mathématiques et servante des sciences naturelles. G. Bell & Sons Ltd.
1966 (24 octobre 1996 ou 1998)
Bell, Marc. Marc Bell
Présente le monde magique de M. C. Escher. Musée d'art de Boca Raton
20 janvier – 11 avril 2010 (15 décembre 2014)
Nominalement un répertoire d'un
Exposition Escher au musée d'art de Boca Raton, bien que
nature d'un livre. Ayez de nombreux dessins inédits tirés de microfiches. avec
essais de Salvatore Iaquinta (Le phénomène de la culture pop réticente (sic), Escher
Souvenirs: comment l’Italie a façonné l’avenir & # 39; Carte boussole, Federico Guidiceandrea
(Remplir le vide) et Willem F. Veldhuysen (L'œuvre magique de MC.
Escher « ). Celui d’Iaquinta sur l’impression "Compass Card" est intéressant, bien que
Si ses observations / hypothèses sont correctes, il faut une confirmation.
R. C. Le livre de jeu. Marshall
Cavendish Books Première impression 1979, deuxième impression 1983. (26 juin 2016)
Une présentation somptueuse souvent citée comme la bible des jeux de société.
Bien que les jeux de société ne suscitent aucune inquiétude déraisonnable, j’en ai un
intérêt passager, et environ la moitié d'entre eux sont étonnamment nouveaux. rien
en particulier de nature mathématique, bien que bien sûr il n’y ait aucune raison de
—-. Découverte de l'ancien conseil
jeu. Shire Publications Ltd 1980 (18 février 2007)
Livre de poche petit format.
Bellos, Alex. Alex & # 39;
Aventures à Numberland. Dépêches du monde merveilleux des mathématiques.
Bloomsbury Publishing Ltd, 2010. Titled in the US as Here’s Looking at Euclid. (27 July 2014).
A personal wander around
mathematical aspects of interest to the author, of an overwhelmingly popular
level. Occasional references to Escher, pp. 244 and 392 hyperbolic geometry,
with Circle Limit IV. Phi, pp. 299-301 (and colour plates), with Gary Meisner
interview. Martin Gardner pp. 250-253, plus lots of general interest. Sam Loyd pp.
237-240, Henry E. Dudeney pp. 240-242. Typical Bellos, of a delightful read.
————. Can You Solve My
Problems. A case book of ingenious, perplexing and totally satisfying puzzles.
Guardian Books, 2016 (3 February 2018)
Described as, in the
introduction, ‘… a curated collection of 125 brainteasers from the last two millennia, linked with stories about their origins and influence.’
Bellos, Alex and Edmund Harriss. Snowflake Seashell Star. Canongate Books Ltd, 2015 (September 2015)
Mathematical coloring book,
not paginated. Of note is my contribution to this, of the fish tessellation on back
cover and two works inside; ‘Nested Fish’ again, and ‘Interflocking Birds’
(Bellos' witty description). Of note is Harriss' parquet deformation (with likely Bellos
title) ‘De-four-mation’, of four non-periodic tilings positioned in a corner,
which morph left to right and top and bottom. Beat that if you can!
Belur, Ashwin and Blair Whitaker. A Practical Solution to
Rubik’s Magic. Corgi Books 1986 With a foreword by Erno Rubik. (Two copies,
27 September 1992 and 5 February 1994)
Small format paperback, of
just 32 pp. Gives instructions as to Rubik’s Magic, a latter day addition to
the cube theme, perhaps best described of a folding rectangular 2 x 4 array and ring premise. From memory, I
do not believe I have ever tried ‘seriously’ to solve this.
Seeing as I was unfamiliar with
Belur and Whitaker I had a look on the web. Apparently there was controversy
with Rubik, despite him writing the foreword. Fra The New York Times, 20 October
Dr. Erno Rubik, the Hungarian inventor who bedeviled
millions when his beguiling Mondrian-colored cube became a phenomenal best
seller in the early 1980's, is himself bedeviled by two University of Pennsylvania
computer-science graduate students who are cashing in on the spiraling
popularity of his newest brain twister, which has been on the market for only
The first of 500,000 copies of a 32-page book by the
graduate students explaining how to solve the new puzzle, Rubik's Magic, are to
be shipped Monday to bookstores around the country, several months before the
inventor can finish his own book containing the solution. It is scheduled for
publication early next year.
The students, Ashwin Belur and Blair Whitaker, hope
their $2.95 book, ''Rubik's Magic: The Solution,'' will be carried
piggyback on the fast-growing craze for the palm-sized puzzle, a series of
squares and rainbow-colored rings that is mathematically even more difficult to
solve than its predecessor, Rubik's Cube. More than 185 million copies of the
cube have been sold around the world….
Bergamini, David and the Editors of TIME-LIFE Books. Mathematics. Time-Life 1969,
1970. First published 1963 (16 July 1995 Hardback, 21 March 1998 Paperback).
This is really ‘The Story’ of
mathematics, rather than of an expository nature as the title implies. Much
of interest, although detailing this is not the most straight forward task. aucun
tiling. (False) references are made to the golden ratio appearing in paintings,
pp. 94-97, of which Mario Livio in ils
Golden Ratio s. 164 rebuts. For instance, it’s just ludicrous the figure of
This is a paperback, also see
hardback, in possession.
Beyer, Jinny. Designing Tessellations: The Secrets of
Interlocking Patterns. Contemporary Books 1999 (11 December 2007)
Jinny Beyer, a patchwork designer, and not, by nature, a mathematician, or at least a natural one, gives her thoughts on designing tessellations, and much more than the title otherwise suggests. Her background pervades the book, of a patchwork premise. Strictly, I do not know what to make of this. There is the potential for a good book here, but this is not it! In short, I think she addresses too many aspects beyond her understanding (albeit well-intentioned, with the non-mathematician patchwork worker in mind), of which she attempts to cover ‘all’, from history to basics to Escher and more. There are many aspects here that I have issues with. To begin, even the title! There are no ‘secrets’ as such in the sense of information being withheld. Another is the text is lacking in exactness in various places, too numerous to list all. I content myself with her definition of a tile, illustration 1.3, p. 4. Chapter 10, a digression to the Escher aspect, is a veritable disaster. She simply does not understand the issues. Anyone who can be proud of ‘houses’, pp. 206 and 222 reveals her lack of understanding of them. Likely a house, being a popular patchwork motif, was thus obviously chosen, but this does not excuse poor practise in design. The other tessellations, some by others, generally lack merit. However, a cat (by Beyer) ‘Tessellating Sue’ is at least respectable. The ‘pure’ tilings are better in terms of worth. Chapter 11, on Metamorphosis, is not really as such; the transitions are far too abrupt, being nothing more than abutments. Aside from the content per se, the book lacks an index, and so thus finding specific aspects is trying. It really is most frustrating trying to separate the wheat from the chaff here!
Interestingly, the cover and title pages features the Polya tile C4, but without my bird motif.
Has many instances of Escher’s periodic drawings: Birds E128; E120/121 Birds and Fish; E24 Birds and Fish E25 Reptiles, all p. 3; Reptile E25, p. 127; E73 Flying Fish, p. 134; E128 Birds, p. 203, E90 Fish, p. 205, Fish and Boat E72, p. 219; E120/121 Birds and Fish, p. 220; Fish E119, p. 221; Bat/Bird/Bee/Butterfly E81, p. 224, E85, p. 225
Prints: Reptiles, p. 228, Metamorphosis I, pp. 236-237
Sketch: wall mosaic in the Alhambra, p. 202
Cairo tiling, but not attributed as such, p. 144
Bezuszka, Stanley, Margaret Kenney and Linda Silvey. Tessellations:
The Geometry of Patterns. Creative Publications 1977 (15 October 1994)
School age level, with
‘activities’. ‘Skew’ Cairo
tiling, on triangular grid, p. 38. No Escher-like tessellation discussion at
Bibby, John. Mathematics
Resource Guide. No.4 (Year Unstated)
Bigalke, von Hans Günther and Heinrich Wippermann.
Reguläre Parkettierungen. Mit Anwendungen
in Kristallographie, Industrie, Baugewerbe, Designund Kunst Gebundene
Ausgabe – 1994. LOOK FOR,
Bigalke, von Hans. Heinrich
Heesch: Kristallgeometrie, Parkettierungen, Vierfarbenforschung (Vita
Mathematica) (Gebundene Ausgabe) WANTED
Birkhäuser Verlag, 1988 Translated: Heinrich
Heesch: Crystal Geometry, Tiling, Four Color Research, 320 pages.
Billings, Robert W. and Robert Williams. ils
Infinity of Geometric Design Exemplified. One Hundred Designs and their Foundations Resulting From One Diagram.
London 1849 On line (not downloadable), seen at Hathi Trust (24 April 2015)
From a reference in Bradley. Quoted
on p. 6. Of limited interest, if at all. The book is ostensibly about tracery
designs, something of which is strictly outside of tiling matters. Tracery (rather
than tiling) seems to be Billings’ main interest, he has one other book, at
least, on the subject.
————. The Power of
Form Applied to Geometric Tracery. London 1851. (24 April 2015)
From a reference in Bradley.
Of limited interest, if at all. See comments above.
Bilney, Bruce. Plato’s Jewels. The Five Regular Solids.
OZZigami Pty Ltd 1997 (19 February 2010)
Gift of Bruce Bilney. Self-published
booklet of 32 pages. Promoting his own ‘Spectrochrome’ Platonic models. Occasional
digressions from polyhedra, with stereo and tessellations.
Bingham, Jane. Illusion Art. Heinemann Library 2008 (17
November 2018, Cleethorpes Library)
as for teenagers on the back cover. A look at various aspects of illusion art,
of 56 pp. A somewhat lettvekt treatment. M. C. Escher features prominently,
of 16-17 (primarily), 20-21, 35, 40-42
(in passing) and cover (Waterfall). However, the research is
particularly poor here, with Escher described as from Belgium! And the ‘find
out more’ page gives J. L. Locher’s name as Locker, and misspells Doris
Schattschneider without the n. From this, likely they will be other errors gjennom også. The book is perhaps atypical of others, in the illusions shown
many I have not seen before, and with a name I have not seen before, notably
with John Kay, p. 39, of ‘The avocat and the Client’, although I am fortrolig avec
the illusion. The section ‘puzzling patterns’, pp. 40-43 discusses tessellation, with an illustration
of Patrick Snels' work. Overall, even for
a teenager, far too lightweight.
Birtwistle, Claude. matematisk
Puzzles and Perplexities: How to Make the Most of Them
Allen & Unwin, 1971. First saw c. 23 July 1987. Not in
A book that was briefly studied
in 1987, but is of no consequence. Unavailable, save for a mad price, £180!
Blackie, Alex B. Wood Pavement; Its Origin and Progress, London, Sherwood, Gilbert and Piper, 1843. Available Online. (c. 8 May 2019)
Of pavement interest. On wood block paving. Everything one would wish to know! (Skim Read). Reference to hexagonal blocks, pp. 25-26, 28, 35-36, 39, ‘41’, 48-49, 54, 56, 72. David Stead mentions.
Block, J. Richard and Harold E. Yuker. Can You Believe
Your Eyes? BCA 1991 (14 September 1996)
Not mathematical per se, but
as it includes maths related aspects, such as ambigrams, I thus include here.
Very pleasing indeed. 20 chapters, replete with interest. To list favourites is
Bonanni, A. P. P. Ricreatione
dell’ochio e della mente, nell’Osservatione delle Chiocciole, Roma, 1681
Circle packing reference, as given by D’arcy Thompson
Bourgoin, J. Arabic Geometrical Pattern & Design.
Publications, Inc.1973. (9 April 1993)
Boles, Martha and Newman, Rochelle. Universal Patterns.
Book 1. Pythagorean Press 1992 (19 November 1994).
The first of a * book series. C'est
somewhat difficult to describe the premise of this book, due to a fragmentary
nature of topics covered; likely aimed at a secondary school level. Prominent
throughout are ‘compass constructions’, of a basic level, useful as an
immediate resource. Occasional reference is made to pattern in the real world. note
that this a book on patterns in the general sense; that is, it is not focussed
Boles, Martha and Newman, Rochelle. The Surface Plane.
Book 2. Pythagorean Press 1992 (3 June 1993)
Similar in spirit to Book 1,
with compass constructions. Of the two, this is more directly related to my
interest, with chapter 4 on tiling, pp. 130-169, and other tiling instances
scattered throughout the book.
Bolt, A. E. and J. E. Hiscocks. Machines, Mechanisms and Mathematics. Mathematics for the
Majority. Chatto & Windus, 1971 (22 August 2004)
One book of the seven-part
‘Mathematics for the Majority’, series, of which I have two. The book seems to
have been compiled by a ‘project team’, with one primary author stated. ils
books are stated as ‘Chatto & Windus for the Schools Council’, which thus
gives the intended audience. The topic of this book is out of my mainstream
interest, but it still has isolated aspects of interest. Also see Mathematical Patterns by T. M. Murray-Rust
for another in this series. Note that patterns here is used in the broad sense,
and is not of tiling.
Bolt, Brian. The Amazing Mathematical Amusement Arcade.
Cambridge University Press 1987 (9 June 2002)
130 ‘popular’ mathematical
puzzles, with answers. Stated as from ‘a ressurs book written for teachers’,
but the title is not given. Possibly, cette is the reference below. Also states ‘many of the puzzles have a very long
history, other are original…’. However, upon an admittedly cursory look, I
cannot see any that I am not familiar with. No plans to re-read, being one of
many of the same compilation nature.
————. Mathematical Activities. A resource book for
University Press 1987 (18
154 activities, of a
recreational nature, pitched at a middle school level, with answers. Especially
see Activities 39 Tessellations, p. 28 and Activity 40, Tessellations and art,
s. 29. Has Escher’s Swans and Horseman periodic drawings. Unfortunately, Swans
is overlaid with an incorrect grid. Also answers pp. 147-148 beginners, any
quadrilateral will tessellate rule. Also see Activity 76 The Pentominoes, pp. 56-77.
Other aspects are of interest.
————. A Mathematical
Pandoras Box. Cambridge University Press, 1993 (27 June 2016) PDF
Seems to be, as with his other
works, a compilation from other sources.
Bossert, Patrick. You Can Do
the Cube. Puffin Books 1981 (27 September 1992)
Small format paperback, of 112
pp., brought out at the height of the Rubik Cube craze. Simple step-by-step
instructions. However, although I have likely tried this at the time, this was
to no avail! The situation has not
progressed since then, not that I have tried for a long while. As much as I
would like, time forbids a new round of study. Je
see that Bossert was just twelve-years-old at the time! What became of him is
Boyer, Carl B. A History of Mathematics. (Second
edition, revised by Uta C. Merzbach) John Wiley & Sons Inc. 1991 (25 April
Boys, C. V. Soap Bubbles Their colours and forces which
mold them. Dover Publications Inc. (19** reprint of 1959 edition) (18
Bradley, Amos Day. ils
Geometry of Repeating Design and Geometry of Design for High Schools.
Bureau of Publications
Teachers College, Columbia University, New
York City. 1933, and 1972 reprint. (17 January 2011)
As oft quoted by Doris
Schattschneider. What is Bradley’s own
work or not is not of the greatest clarity; I suspect he is borrowing from the
other references. Has much of renter.
P. 123 Cairo-like diagram, dual. Has a good bibliography.
Bradley, Chris. Cairo.
Berlitz pocket guide. Berlitz Publishing/Apa 2008. (24 April 2016)
Possible Cairo tile sighting
at Azbakkiyyah Gardens, p. 28.
Brandreth, Gyles. ils
Big Book of Optical Illusions. Carousel Books 1980 (7 September 1997).
Juvenile. Standard fare.
Not a ‘big book’ at all;
standard paperback size!
————. The Big Book of Puzzles and Games. Treasure
Trykk. (First Published in Great
Britain as four separate titles by Carousel
Books) 1989. (Day not stated, July 1999)
————. The Complete
Puzzler. An ingenous compliation of tricky riddles and cunning conundrums.
Panther Books,1984. First published de
Robert Hale Limited, 1992.
(Possession date not recorded)
A part opprinnelig, part from
other sources small format paperback compilation, as is made clear in the
foreword, including puzzles of Lewis Carroll, Sam Loyd and Henry Dudeney,
although the attributions not made clear in the puzzles themselves. Brandreth’s
‘originals’ seem few and far between. Has 20 various puzzles within the full
remit of the term. Dissection puzzles pp. 39-43, Geometric Puzzles pp. 54-56,
Pentominoes pp.87-92. In style, the book is similar to many other compilations.
In short, a fun work, not of a scholarly nature, having not seen it referenced.
Brest, Hillary et al. The Stella Octangula Activity Book.
Key Curriculum Press 1991. (30 April 1994)
Various activities and investigations
of the Stella Octangula, including blackline masters (nets)
Also see companion book The Platonic Solids Activity Book, Ann E.
Fetter et al.
Brett, Michael, and Werner Forman. The Moors: Islam in the West. HarperCollins 1984.
(Seen c. September 1987, but not in possession).
Note that this book (title
only) was recorded on a menu card, stated from the central library, in
conjunction with other Islamic tiling books of the day, 1987. There is no
recorded studies as such. I cannot now recall this in any way.
Briggs, William. Second Stage Mathematics. ils
Organised Science Series. University
Trykk. c. 1900? (20 June 1993)
Typical generic maths text
book of the day; way beyond me, on Euclid, Algebra and Trigonometry. One of
many that I have; simply, one would have sufficed. The reason for obtaining the
book was to be able to look up any maths/geometric construction as and if
required, but I do not believe that I have used this in any way.
Bringhurst, Robert. The Elements of Typographic style Second
edition. Hartley & Marks, publishers. 1992 (3 November 2018)
Some ‘page size mathematics’
Chapter 8, pp. 143-178.
Briscoe, Susan. The Ultimate Sashiko Sourcebook. Patterns, Projects and Inspirations. David and Charles 2005. Cleethorpes library. First saw a few years ago, but never got around to borrowing (16 February 2019)
Simply stated a book on ‘Sashiko’, a term of Japanese hand stitching. Sashiko (pronounced shash-ko) literally meaning 'little stab' or 'little pierce' is a traditional Japanese hand stitching technique that can be used to strengthen, repair, add warmth to or simply decorate fabric refers to the small running stitch that is worked to build up distinctive decorative patterns, of which there are hundreds. The book begins by exploring the origins of the technique to strengthen clothes and to make them warmer. Getting Started describes everything you need to begin stitching, including selecting suitable fabrics and threads, marking out patterns on the fabric, as well as the stitching technique itself. Ten project chapters show how easy it is to use sashiko patterns to make beautiful items for the home. The main focus of the book is the step-by-step detail in the pattern library, showing you exactly how to mark and stitch each individual pattern with ease. Finally a gallery of work by contemporary Japanese textile artists from Yuza Sashiko Guild provides extra inspiration.
Although inself, from the title alone, one would not expect this to be of any real interest, the book is replete of tiling patterns, and so worthy of study. Further, as such, it is invaluable (i.e. readable) in the Japanese-English context. Especially see p. 67, ‘Yatsude asanoha’ (eight-lobed hemp leaf) from which a Cairo tiling can be derived. P. 87 has a tiling that can be shaded as a outstretched human figure! Furthermore, for the first time (I believe) I have realised that what appears to be traditional Japanese patterns of an isometric appearance are not so, but rather are drawn on a rectangular grid.
Biography: Susan Briscoe is a textile artist, quilter, teacher and author of numerous books.
Brockett, Anna. Draw Patterns.
Adam & Charles Black 1981. (15 May 2005)
Juvenile, 12+. No Cairo.
Brown, James. Shiny
Touch Farm. Bibliographic detail is next to non existent. Web research
gives 2011 and publisher Walker (13 or 20 April 2013)
Minor tessellation reference
of a dog. An infant’s book, found by pure chance upon a visit to Cleethorpes
library, where in the sale section this was placed prominently, my attention
drawn to a symmetrical drawing of cows on the front cover. Various other
animals (pigs, sheep, duck, horse) are arranged ‘close fitting’ in a
symmetrical arrangement. Curiosity aroused, upon looking inside, a tessellation
of a dog, seen before, on the internet, but by whom I can’t recall.
No credit was given in the
book. Symmetry is evident throughout the whole book, of just 12 pages, but the
dog is the only tessellation per se.
Brown, Richard (ed.). 30-Second
Maths. The 50 most mind-expanding
theories in mathematics, each explained in half a minute. Ivy Press, 2012
(18 March 2017)
Popular account. avec
contributions by Richard Brown, Richard Elwes, Robert Fathauer, John Haigh,
David Perry and Jamie Pommersheim., No tessellation. Disconcertingly Brown
himself (presumably) makes a schoolboy mistake on matters of astronomy,
referring to the ‘dark side of the moon’ (meaning the far side), p. 83. Has
isolated instances of interest.
Brown, Richard G. Transformational Geometry. vallée
Seymour Publications 1973. (24 October 1998)
Escher’s periodic drawings on
cover, swans, and p. 36, Beetles and Flatfish p. 45, Swans, and p. 83 Fish. qui
such, there no tiling per se whatsoever! Discuses algebraic operations, which
goes over my head, or at least as I so desire to study.
Brissenden, T. H. F. Mathematics Teaching. Theory in
Practice. Harper & Row, Publishers, Ltd 1980 (19 February 1998).
The thinking behind teaching.
Britton, Jill and Walter Britton, Teaching Tessellating
Art. Activities & Transparency Masters
Dale Seymour Publications 1992 (9 February 2010)
Aimed at a school-age level,
12+ years. Much use is made of Escher's work, both tessellations and prints, E
25, 35, 44, 63, 67, 75, 96, 97, 104, 105, 117, and Reptiles, Metamorphosis I.
Use is made of students’ work, the quality of which varies. Broadly, it
discuses procedures for creating Escher-like tessellations, and also with early
computer programs, now somewhat dated.
Bronowski, Jacob. The Ascent of Man. British
Broadcasting Corporation 1976 (24 October 1993)
Chapter 5, The Music of the Spheres pp. 155-188.
Buchsbaum, Ralph. Animals Without Backbones. University of Chicago Press. Eleventh Impression 1947. First published 1938. (May 2019). Available on the Internet Archive:
Of peripheral Escher interest. Said (and confirmed by Sherry Buchsbaum, the daughter of the author in a reply to a blog posting, below), to be the book that Escher used for his Flatworm drawing references. Although obviously non Escher per se, it is included here in relation to him. From Sherry Buchsbaum:
Escher was definitely influenced by Elizabeth Buchsbaum's drawing of planaria. This can be seen in the chapter heading drawing for Chapter 10 and 12 and following drawings in Animals Without Backbones… Chapters 10 p. P.109, Chapter 12 p. 124.
From Amazon: Animals Without Backbones has been considered a classic among biology textbooks since it was first published to great acclaim in 1938…
Vielecke und Vielfläche: Theorie und Gesschichte. (Translated: Polygons and
Polyhedra) Leipzig: B. G. Teubner, 1900 (Downloaded from Internet archive
10 April 2015)
quoted in tiling concerns, such as by Schattschneider. On polyhedra. Highly
technical, with much abstruse text, albeit liberally illustrated with line
drawings, and latterly plates and polyhedral models. Of interest as regards
tiling p. 109 dual tiling (Cairo) p. 158.
Buckwell, Geoff. Mastering
Mathematics. Macmillan master series. Macmillan 1991. (11 September 2000)
Textbook, for beginners, of a
broad range, with the equivalent of 2 + 2 to calculus! Minor tessellation pp. 94-95,
with one diagram is of interest, in that this stumped me in my early days (in a
different book), of a octagon and two squares, as a unit to be tiled. Or was it
a octagon and one square?
———— . Work out GCSE
Maths. Macmillan (September 1987?)
Note that I have various
doubts as to this book, recorded on a shared sheet filed in Cundy and Rollett. Seemingly,
part of a series, although the chronology does not correlate…
Bunch, Bryan. Reality's Mirror: Exploring the Mathematics
of Symmetry. New York: Wiley, 1989. (13 September 2014)
From an Escher reference in Schattschneider’s
Visions…. Somewhat disappointing in
this regard, with a most lightweight treatment indeed of Escher, with two small
discussions, as ‘Eschervescence’ Part 1 pp. 81-85 (Fish and Frog
Optimist/pessimist Birds and Fish) and Part 2 pp. 118-121 (Pegasus, Birds) but without
any new insights. There is one enigmatic matter concerning a tessellation of
Escher's (Pegasus) in which Bunch states, p. 120 ‘… once flew along the cover
of a book on crystals…’, but this is not sourced. I am unfamiliar with this. sur
looking for Bunch’s details online to ask him, of an initial look, as of 2017 there is nothing on him. he appears to
be more of a science writer than a mathematician per se. The book itself is
very much in the spirit of Gardner’s ils
Ambidextrous Universe, of which in the preface Bunch defers to.
Burden, I., J. Morrison, John Twyford. Design & Designing? Longman 1989? (17 January 1989)
As such, there are various uncertainties here as to the book, borrowed from Grant Thorald library, due to it being poorly referenced of the day. Upon a internet search, I have only found one other book with this title, but as this is a subsequent publication to the date recorded here, 17 January 1989, it cannot be this one. Further, I am not even sure of the title – a page number precedes the title, and so possibly this is a chapter reference instead. No publisher was given.
Whatever, the book can hardly be of any importance; the study, on a 10 January 1989 sheet headed by A. Racinet ornament studies, consists solely of a well-known jigsaw tiling seemingly traced in which I remark upon the opposite side square feature.
Burn, Bob. Sorting by Symmetry. Patterns with a Centre.
Association of Teachers of Mathematics 2005. (13 June 2009)
As sent by Bob Burn.
————. The Design of Tessellations. Cambridge University
Press 1987 (14 April 1993)
Non-attributed Cairo tiling, sheet 30, shown
as line drawing, equilateral, no text. Drawing tessellations on a microcomputer,
the BBC (B).
Burn, D. V and E. W. Tamblin. Arithmetic Itself. A Junior
Teach Yourself Book. English Universities Press, 1965 (First saw, or at
least date recorded, of 16 September 1987, College library)
A brief, single-page study, of
which my recollections have faded to essentially nothing, with the book of a
junior audience. The book is not in my possession, nor was the page photocopied
of the day. Some minor tiling, albeit still of interest.
Burns, Marilyn. The I Hate Mathematics! Book. Cambridge University Press 1987. (not stated,
Burrett, Anthony. Mathematics
in Time and Space. Peter Haddock Ltd. 1973. Project Club Booklet (25
Small (square) format
paperback, 66 pp. From the 200-book Project Book series, introducing all kinds
of pastimes from brass rubbing to building a home museum, with here mathematics
of book No. 110. A handful of titles blossomed into a range of two hundred as the
lavishly illustrated booklets caught on. An emphasis is on the practical
aspect. The series is aimed at school children, c. 12 years of age. Mostly about time per se. Polyhedra pp. 46-47, Minor
tilings pp. 48-49. However the treatment is so basic as to be of no consequence.
Also see book No. 101, Mathematics for the 1970s, not seen.
Cadwell, J. H. Topics in Recreational Mathematics. Cambridge University Press 1966 (13 October 2006)
First saw in Grimsby central library September 1987.
Occasional aspects of interest,
largely of a popular level; Chapter 1 Regular Polyhedra, Chapter 9 Dissection
Problems in Two and Three Dimensions, but mostly too advanced. Tessellation
only in passing. Studied in September
1987, very much of the day, and somewhat
excessively, given the content.
Cain, John et al. Mathematics Miscellany. A source
book for teachers. British Broadcasting Corporation 1966. (19 February 1998)
Flatters to deceive as to recreational
maths aspects. Typical 1960s book. of most interest Chapter 7 Geometry, Chapter
8, Three Dimensions, with tessellations. Escher is mentioned briefly, p. 64.
Callender, Jane. 2000
Pattern Combinations. A step-by-step
guide to creating pattern. Batsford 2011 (7 April 2012) Grimsby library
Mistakenly states that there
are ‘20 demi-regular tilings’; page 9; a howler, as noted as by Helmer Aslaksen
in his Bridges paper.
Calvert, Albert F. Moorish
Remains in Spain. Being a Brief Record of the Arabian Conquest of the Peninsula
with a Particular Account of the Mohammedan Architecture and Decoration in
Cordoba, Seville, &Toledo. London: John Lane, Bodley Head. 1904 (Downloaded from internet 5 May 2015)
Of note is the length of this
book, 586 pages! On mostly, Cordoba, Seville and Toledo, which concerns
architecture, and so of limited appeal, although a most interesting chapter on
Moorish ornaments is on page 479 onwards, with many ‘simple’ tessellations I was
unaware of. One to study.
————. The Alhambra.
George Philip & Son London 1904 (Downloaded from internet 6 May
From a reference in Grünbaum. qui
such, this is very much like any other book on the Alhambra of the day; vous
seen one, and you’ve seen then all. Again, another weighty tome, of 464 pages.
That said, was as unfamiliar with the tiling on p. 303 (521). P. 341 (558) could
arguably be interpreted as a forerunner of Escher’s Other World print, likely he would have seen this viewpoint on his
Alhambra visits, of which in later years may have rekindled in his print.
Campbell, Cyndie. M.
C. Escher. Letters to Canada, 1958-1972. National Gallery of Canada Library
and Archives Occasional paper No. 9. 2013 (10 December 2013)
A collection of letters from
M.C. Escher to his son, George. Full of interest, with many new names not
previously known. Padded out a little with commonly seen photographs and prints
of Escher, though that said, there are the occasional photograph not having
been seen. Introduction by George Escher.
Mathematischen Beiträge zum Kulturleben
der Völker. Halle 1863 (Downloaded from internet 27 April 2015)
From a reference in Bradley. Book quoted on p. 12. Somewhat
of a let down; the book does not have a single diagram!
————. Vorlesungen über Geschichte der Mathematik. Second edition Leipsig
1894 (Downloaded from internet 27 April 2015)
From a reference in Bradley. Somewhat of a let down;
the book does not have a single diagram!
Carraher, Ronald G. and Jacqueline B. Thurston. Optical Illusions and the Visual Arts. Van
Nostrand Reinhold Company New York (30 January 2015). First saw September 1987,
Although not strictly a
mathematical book, this is included here as it was a book I studied right at
the beginning in of my interest in tessellations, in 1987. This was first seen
in Louth library in September 1987, and briefly ‘studied’ there, taking
tracings of the pages of most interest.
part of a concerted effort of eventually returning to old material that
requires original material for updating, I decided to obtain such books from
the period. Also, I note that Locher includes a reference to this book in
regards of Escher, and so there was also the prospect of an Escher piece as
well, although upon receiving the book this is a decided let down, of a single
picture, Relativity, p.95, with minor
my memories of the book had dimmed. As such, it is not of a great deal of
importance. Interesting, yes, and indeed with the occasional new aspect (such
as a Dali sketch), but not in any way fundamental to tessellation studies.
Chamber, W. R; Murray, John. Shape and Size. Book 2.
Nuffield Mathematics Project. Newgate Press Ltd 1968 (9 June 1996)
An arbitrary part series of a
uncertain series, possibly of a series of four books. Juvenile, with instances
of their work from the book. Occasional tessellation 36-45. In relative terms,
of more interest is Book 3, Shape and
taille, confusingly of the same title. Of limited use in terms of
innovation/usefulness, which is to be expected give its intended audience.
Chamber, W. R; Murray, John. Shape and Size. Book 3.
Nuffield Mathematics Project. Newgate Press Ltd 1968). (2 June 1995)
Juvenile. Tessellations front
and back covers. Chapter 5 Tile patterns – Tessellations 27-28; 32-41, Chapter
7 More about polygons and tessellations 32-42. Includes studies of irregular
pentagons! Of limited use in terms of innovation/usefulness, which is to be
expected give its intended audience.
Chamber, W. R; Murray. Environmental Geometry. Nuffield
Mathematics Project. Newgate Press Ltd 1969. (Teachers’ Guide).
Juvenile. This seems related
in someway to the Shape and Size
books above, although there are indeed differences. loosely on a premise of
architecture. Whatever, of limited use in terms of innovation/usefulness, which
is to be expected give its intended audience.
Chauvan, Sumi Krishna. Delhi,
Agra & Jaipur. The Golden Triangle. First published in 1982 by Roloi
Books International. 1988 (19 July 2014)
Although not a maths book,
included on account of it containing some geometries of India, notably a
possible Cairo tile sighting (now known not to be so) at Fatehpur Sikri at the
Panch Mahal or Wind Tower, p. 65.
Christie, Archibald H. Pattern Designing. Oxford at the Clarendon
Trykk. 1909? (6 August 1994)
The full title inside reads
‘Traditional Methods of Pattern Designing An introduction to the study of
decorative art by Archibald H. Christie with numerous examples drawn by the
author and other illustrations’. The majority of the book is of ornament and
patterns per se, rather than of tessellations. A whole chapter refers to
counterchanges, Chapter 13, pp. 282-298. ‘Pólya’s ‘Do3’ tiling is shown, p.
296, Christies’ predating this, and Meyer of 1888 thereof. Page 133 gives the
derivation of ‘Cosmati’, from Laurentius Cosma, of the thirteenth century.
Checked for any references to Cairo pentagon and par
Clegg, Brian. A Brief
History of Infinity. The Quest to Think the Unthinkable. Robinson, 2003 (6
Has an Escher print on the
front cover, Knots.
Cook, L. H. Longley-. New
Math Puzzle Book. Van Nostrand Reinhold 1970 (14 January 2017)
A ‘favoured chance’ finding
whilst web searching. A relatively lengthy, although a little lightweight chapter
on tessellation, Chapter 7, 109-131. This includes minor Escher-like aspects,
pp. 112, 117, 120. Incidentally, the related diagram on p. 127, titled as a
‘gingerbread man’ showed up upon a search, of which, although not stated, this is
likely taken from MacMahon, p 108, of the utmost significance to me, as it
underpins one of my own favourite human figures. On this diagram alone, I
decided to pursue the book, with the chapter on tessellation a pleasing bonus.
Cook seems to be a keen promoter of recreational mathematics, although no
bibliography or index is given. Escher (incorrectly spelt) is mentioned in
Coen, Enrico. The Art
of Genes. How organisms make themselves. Oxford University
Press, 2000. C. 2005-2008? – Date has faded; I have had this for many years; it’s
certainly not in the last couple or so, say.
As such, this is not a maths
book, but as it includes ‘occasional Escher’ I include for the sake of
‘everything Escher’. Escher aspects, 1-2, 137, 312-313. Drawing Hands 2, Circle Limit
Je 137, Balcony 313.
Coffin, Stewart T. The Puzzling World of Polyhedral
University Press 1991. (3
Delightful throughout. aussi,
two-dimensional puzzles and dissections are briefly discussed, Chapters 1 and
Cohen, Jack; Stewart, Ian. The Collapse of Chaos.
Penguin Books 2000 (12 May 2002).
Colby, Averil. Patchwork.
B. T. Batsford, London. 1987 First published 1958 (18 November 2001)
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed, it is one of the better books there is
on the interrelation between the two, and indeed led to extensive studies of
the day (1987, as indeed with other patchwork books). However, now, and for
some considerable time, the nature of the material is considered hardly worthy
the time originally devoted to it.
Cole, Alison. Perspective. Dorling Kindersley 1993.
Includes Escher’s Impossible World, page **.
Cole, Drusilla (General Ed). 1000
A&C Black 2003.
Conway, J. H. On Numbers and Games. Academic Press
Ltd. 1976 (14 September 1996)
Of limited interest, mostly
J. H. et al. The Symmetries of Things. A. K. Peters Ltd 2008 (19 March
Decidedly advanced for me!
Escher plane tilings 67 Horseman, 22 Bird and Fish, 70 Butterflies, Circle Limit
IV, pp. 134-135, 152, 153, 224
Scholarly discussion of Angels
and Devils 224. Cairo
tiling apparently projected on a sphere, front cover and repeated page 74.
First saw this book, briefly, at Bridges Leeuwarden, 2008, with a false first impression
at the time that it would be suitable/useful for me.
Corbalán, Fernando. ils
Golden Ratio. The Beautiful Language of Mathematics. Published by RBA
Coleccionables, S. A, 2012. Appears to be a English translation of a Spanish
work (7 June 2014)
Section on periodic and
aperiodic tiles, pp. 76-87. Escher aspects: Spiral,
s. 65 and two bird motifs p. 81
On occasions shows bizarre
golden ratio overlays, such as pp. 12-13, 107.
Cordova, Chris De. The Tessellations File. Tarquin
Publications. 1983 (3 June 1993)
Juvenile, for classroom work.
Very basic indeed, pp. 1-6 are given largely to explanations, the rest of the
book is of tilings on single pages, without any apparent structure. un
instance of Escher-like tessellation, page 6, a human figure drawn without
understanding of the issues, and which is particularly poor.
Costello, Matthew J. The Greatest Games of all Time.
John Wiley & Sons Inc. 1991. (27 August 1997)
Cotterill, Rodney. ils
to the Material World. Cambridge
University Press 1989.
(Date has irretrievably faded, c. 1995).
Although not a maths book per
se, included as it has Escher aspects. Page 63 E97 Bulldogs, E85, Lizard Fish
Bat; 81 Print Gallery.
Courant, Richard and Herbert Robbins. What Is Mathematics An Elementary Approach
To Ideas And Methods. Oxford University Press, U.S.A. Second Edition 1996, revised
by Ian Stewart (26 May 2017) Internet download
Cowen, Painton. Rose Windows. Thames & Hudson 1990
(21 May 1994, Sheffield)
144 pp. A4 paperback. Popular
account, with diagrams and photos. Although I have no particular renter en
rose widows per se, there is a decided geometrical element to this, and so thus
likely chose to purchase, in Sheffield, on the basis of ‘buy or lose’ of the
day, this preceding ready tilgjengelighet on the internet. However, I do not
recall any direct study from this. Time forbids a dedicated re-reading. côtés
of interest include p. 93 on Honnecourt with tilings. Geometrically of interest
is ‘Divine Geometry’, pp. 121-127. Incidentally, suitably recalling Honnecourt,
I had a look on the web for any more tilings of his, but it can quickly be seen
that tiling was only a minor interest.
Also see a more substantial
publication, The Rose Window Spendour & Symbol by the same author.
————. The Rose Window.
Splendour & Symbol. Thames &
Hudson 2005, Oversize. (26 May 2014)
Although a most pleasingly
produced book, this is somewhat of a disappointment mathematically. A single
chapter is devoted to the geometry, but this is most brief indeed, of pp. 241-263,
and with most simple constructions given, such as bisecting an angle! beaucoup
references to local cathedral, at Lincoln.
Coxeter, H. S. M; M. Emmer, R. Penrose, and M. L. Teuber,
Eds. M.C. Escher: Art and Science. Amsterdam:
North-Holland 1986. (30 April 1994)
A collection of essays; indispensable.
Coxeter, H. S. M. Regular Polytopes. Dover
Publications Inc., New York, Third edition 1973. The first edition is 1947, the
second edition is 1963 (30 April 1994)
An earlier edition, of 1963?
has the Cairo
tiling featured on the front cover. As a broad statement, the book is too far
advanced for me. Chapter 4, p. 58-73 is on tessellations and honeycombs, albeit
there is nothing here that I can use in any meaningful way. Other chapter on
related interests, Chapter 1 Polygons and Polyhedra, p. 1-13 and Chapter 2
Regular and Quasi-Regular solids, p. 15-30 and Chapter 6, Star-Polyhedra p.
93-114 are all of a similar nature. One aspect of interest that I can follow is
that each chapter ends with ‘historical notes’. Finally, the book has an excellent
bibliography, full of obscure books.
————. Introduction to Geometry. John Wiley &
Sons, Inc. Third Printing, 1963 (24 August 1996)
Academic. Escher pp. 57
(Horseman E67) – 59 (Beetles E91), 63. Very brief text. First studied, or at
least recorded 25 January, and 5 February 1988 upon ordering from the
library. Unsurprisingly, very little is disponible to me.
S. M. and S. L. Greitzer. Geometry
Revisited. Of entire book! 1967, Fifth printing (30 January 2012)
Cracknell, A. G. and G. F. Perrott. Intermediate Geometry.
University Tutorial Press Ld (sic). Third impression 1940, when it was first
published is oddly not stated (23 September 2001)
Typical generic geometry text
book of the day, one of many that I have; simply, one would have sufficed. I do
not believe that I have used this in any way; the material being mostly beyond
my understanding. Very much of its day. Chapter 10 is on polyhedra. Some nice
renditions of polyhedra pp. 147-150
Cracknell, Arthur P. Crystals and their Structures.
Oxford: Pergamon Press, 1969 (First
saw, or at least recorded, 24 September 1987, at college library. Not in
A minor study, in which the crystal studies are
shared with other books of a like nature
Craig, Diana. The Life
and Works of Acimboldo. Parragon Book Service Limited, 1996 (15 Sepember
Although nothing whatsoever on
maths, included here as a tenuous interest as regards cluster puzzles,
specifically of pp. 42-43. I might just add that Arcimboldo is an artist I much
admire, with his work of an Fantasifull nature, although I have not made any
special effort to study his work. This book here, of a popular nature, of a
54-book series (including Escher), found by a casual browse in a charity shop,
at least serves as an introduction pending a more detailed work being found.
Crane, Walter. ils
Bases of Design. London George Bell & Sons 1902. (Read online at
Project Gutenberg, 9 June 2015)
Minor tessellation pp. 89,
128. Arabic designs pp. 213-217, otherwise mostly of ornament. Nothing of any
Crilly, Tony. 50
mathematical ideas you really need to know. Quercus, 2007 (13 May 2012)
Popular account from across
the spectrum of mathematics, 1. Zero, 2. Number Systems, 3. Fractions etc.
However, there is no tiling.
Critchlow, Keith. Order in Space. A Design Source Book.
Thames & Hudson. A date of 1969 is given but it is unclear if this was when
first published. The published date is apparently given as 1987, reprinted in 2000
(22 September 2007)
Barely readable, in that
Critchlow has a belief in mystic, Eastern, philosophical leanings that
permeates the book. Buckminster Fuller has heavily influenced him. Has Cairo diagram p. 49. Interestingly,
in the bibliography, he quotes D. G. Wood, of indirect Cairo tile fame, perhaps
he borrowed from him. This also has an interesting series of diagrams p. 83, best
described as ‘variations’ with Cairo-like properties, with ‘par hexagon
pentagons’ combined in tilings with regular hexagons, similar to Frank Morgan’s
work. I am not totally sure of the originality of Critchlow’s work here. Repeats
the fallacy of 14 demi-regular tilings, p. 60.
Patterns. An Analytical and Cosmological Approach. Thames
Reprinted 2004. First paperback edition 1983. (17 May 2013) Kaplan gives a 1976
Somewhat quirky; Islamic
patterns interspersed with nonsensical cosmological and philosophical speculations
Cromwell, Peter R. Polyhedra. Cambridge University
Press 1997 (10 August 2006)
Escher pp. 2, 171-172 (sketch
of a cutaway view of small stellated dodecahedron), 239, 251, 258. Mostly minor
text, in conjunction with polyhedra.
Crook, Diana (editor). Mrs
Henry Dudeney. A Lewes Diary 1916-1944. Tarturus Press 1988 (20 February
Alice Dudeney’s diaries, with
Henry Dudeney puzzle interest. Quite how this publication came to my attention
is not clear, but likely from Federickson’s writings; it is mentioned in Hinged Dissections. Typically, I did not
pursue this immediately. Of biographical interest concerning Henry. No puzzle
discussions as such, but of the man in the round. As such, I was initially
planning only to read that of Henry himself, but upon reading the book in the
round for a better appreciation decided to read all the way through. A
delightful coffee-time read, a chapter a day, of which I approached each day
avec vigor. I warm to Alice. Her devotion to her dogs is admirable. Also the
privations of war-time stories.
Crowell, Robert A. Intersight One. State University
of New York
1990. 10. Students' work from the Basic Design Studios of William S. Huff
80-85. (8 May 2003)
Delightful. Works by Jacqueline Damino Right, Right, Left, Left; Fred Watts, Fylfot
Flipflop; Rodney Watkins, In Two
Movements; Darren Moritz, Enlarging on
Four Points; Aleaandria Gelencsear, Hex-baton;
Muarizio Sabini, Venetian Net
Cruys, Sander Van de, and Johan Wagemans. ‘Putting Reward in
Art: A Tentative Prediction Error Account of Visual Art’. i-Perception, vol. 2, 9: pp. 1035-1062. 2011.
Non-tessellating article, with
a one-line mention of Escher, p. 1042, illustration with Day and Night.
Cundy, H. Martyn and A. P. Rollett. Mathematical Models.
Oxford University Press 1977 (?) First
published 1951 (First saw 1986 or 1987, college library, studied beginning 21 September 1987)
Of a mixed degree of relevancy
to me; some parts are of the utmost interest, whilst others are way beyond me.
‘Models’ is used in the broad term; it contains much recreational aspects of
tenuous connection to the term, such as geometric dissections, although
naturally polyhedra are indeed to the fore. Of most note is that of Plane
Tessellations, Chapter 2.9, pp. 59-65, largely on semi-regular tilings. aussi
has a Cairo tiling
diagram but naturally without the attribution, page 63. Note that this is not
original with Cundy and Rollett, but is rather taken from MacMahon’s work, as
they state themselves. A strong chapter on dissections, pp. 19-26. (Arthur
Daintith, John and R. D. Nelson. (editors, with ten contributors).
ils Penguin Dictionary of Mathematics. Penguin Books, First published 1989
(4 November 2000)
A more advanced treatment,
aimed at ‘… first-year university students’, with over 2800 entries and more
than 200 short biographies, although nothing, surprisingly, on tessellation!
Primarily of text, has few illusions, with much beyond my understanding and
interest. A useful occasional reference guide, but nothing more.
Dantzic, Cynthia Maris. Design
Dimensions. An Introduction to the Visual Surface. Prentice-Hall Englewood Cliffs, New Jersey 1990 (18
April 1998? The date has faded somewhat).
Brief looks at design aspects.
Much of interest. Leonardo quote p. 308. Numerous Escher pp. 49, 57, 60, 88-89,
103, 137, 252-253.
Paving stone with overlapping
circle tessellation, of c. 700 BC, p. 48.
Mention of Your Hidden Skeleton, with ink blots
designs, of 1900, p 53. Off hand I can’t recall an earlier instance.
Darton, Lawrence. The Dartons: An Annotated Check-list of
Children's Books Issued by Two London. WANTED
Day, Lewis, F. Pattern Design.
London, B. T. Batsford 1979. First saw 27 January 1988, art school library (18
February 2011) First impression 1903, and 1915 and 1923
Similar is style to Archibald
H. Christie’s Traditional Methods of
Pattern Designing, being of ornament
and patterns per se, rather than of tessellations. Of interest, historically, is Erwin Puchinger’s tessellation-like
designs, p. 271. Chapter 6, ‘The Evolution of Pattern’ is perhaps the most
interesting, as it concerns tessellation, rather than pattern as implied by the
title. Nonetheless, there are many other instances of tessellation throughout
————. Textbooks of ornamental design. The Application of Ornament. B. T. Batsford 1898 (20 May 2016, seen
Has houndstooth-like basket weave p. 25. of next
to no tessellation, which only appears loosely.
Part of a trilogy, The Anatomy of Pattern, Planning of Ornament, The Application of Ornament.
————. Ornament and its
Application (17 August 2017 Internet archive download)
The Anatomy of Pattern (1887), The Planning of Ornament (1887),Pattern Design (1903), Ornament and its Application (1904), and Nature and Ornament (1908–9). He published in many
journals, including the Magazine
of Art, il Art Journal et Journal of Decorative Art.
Other books were windows(1897),(3) Stained Glass (1903), Alphabets
Old and New (1898) and Lettering in Ornament (1902).(4)
Davies, Linda and John Hardingham (designers, no author
stated). Leapfrogs Poster Notes. 1986.
Davis, Adam-Hart. Mathematical Eye. Unwin Hyman. 1989
(12 April 1997 and 24 October 1998)
Tessellations pp. 96-97.
‘After Escher’ picture of birds and fish, No. 34, page 97. Juvenile.
Davies, Paul. God and
the New Physics. Penguin Books1990, first published J. M. Dent & Sons
on physics, included here as it has occasional recreational maths. Brief
mention of Escher p. 93, within a discussion of Hofstadter ‘s Gödel, Escher,
Bach. Brief discussion of Conway’s Liv pp. 226-227. Although of a
popular level, most of the text is beyond my understanding (or interest).
Davis, Philip J. and Reuben Hersh. The Mathematical
Experience. Penguin Books Ltd 1988. (19 February 1998)
On mathematical philosophy,
loosely of a popular level. Although widely mentioned in the literature, of
limited value to me; there is no tiling or geometry at my level. Although there
may be the odd snippet of interest, it would be disproportionate as to worth in
time, of 400+ pages in re-reading/re-evaluating the book. I believe Martin
Gardner criticised this book.
Dearling, Alan and Howard Armstrong. The Youth Games Book.
Third edition, Published by I. T. Resource Centre, Glasgow. 1985 First published 1980 (12 July
Paperback, 10 chapters, 247
pp. General puzzles and games of all types (serious and fun) for youths,
seemingly intended for youth clubs. The format is a title and general
discussion. Martin Gardner gets a mention. Largely a rehash of eksisterende games,
from a youth club perspective, but still a welcome contribution in that
context. That said, there is little here that is original. I have no plans to
Deboys, Mary and Pitt, Eunice. Lines of Development in
Primary Mathematics. Blackstaff Press 1986. (9 June 2002).
First seen as a library book,
October 1993. Tessellations: cover, pp. 158-160, 278-286. Ungdoms
Dedron, P and J. Itard. Mathematics and Mathematicians.
Vols. 1 and 2 Methods and Problems. 1973 (translated from French by J. V. Field)
(3 April 1993 and 28 October 1993)
Eclectic account, slim volume.
Kepler plate from Harmonice Mundi, page
53, Vol. 1.
Degrazia, Joseph. Maths is Fun. First Four Square
Edition. 1965 First published 1949. (15 July 1995)
Small format paperback, 159
pp. Gardeneresque. Mostly on number/arithmetic puzzles. No tiling or anything
of a geometrical nature.
Deledicq, Andre and
Raoul Raba. Zoo mathématique, ACL-Les
Éditions du Kangourou, Paris, 1997, 1998,
edition, 2009 (15 December 2017 edition 2002)
little lightweight, of just 64 pages.
Figuring. The Joy of Numbers. Andre Deutsch, First published 1977 (18
the calculating prodigy, a throwback to bygone days of human calculators. On number calculations, and how she achieved such uhyre feats of stupendous calculation. One can only stand back and admire.
Really of general interest only.
Dismore, Julian, Compiler. The Fun and Games Puzzle Book. First
Published Boxtree Ltd, 1990 (25 April 1999)
on the cover as ‘65 brain-teasers from the popular (Yorkshire) TV series’,
although when is not stated, and I’ve never heard of it. Or perhaps I have
forgotten! Whatever, a small format paperback, with puzzles seemingly taken
from existing instances, framed with Dudeneyesque storylines, but typically
much shorter. Dismore is an unknown name to me. The book states that he is an
economist among other lighter interests. Simply stated, the book is like one of
many of the compilation genre, lacking in originality, and so is
Dixon, Robert. Mathographics.
Publications 1991 (10 August 2006)
Dolan, Daniel T.
and James Wilkinson. Teaching Problem Solving Strategies (7 May 1998,
partial PC of a library book. A few pages on polyominoes, nothing of any
significance or substance.
A. Curves. Exploring Mathematics on Your Own 14. 1966 (22 October 2005)
Dörrie, Heinrich (translated by David Antin). 100 Great
Problems of Elementary Mathematics: Their History and Solution. Dover
Publications, Inc. 1965 (24 August 1996). Originally 1958
‘Elementary’ here is relative;
the problems are of a quite advanced nature! Only with a few of these do I even
understand the premise, let alone the mathematics! No tiling as such. Minor
MacMahon references, pp. 9 and 27.
Dresser, Christopher. Principles
of Decorative Design. Cassell, Petter (sic) Galpin & Co. Fourth
Edition. (Downloaded from Project Guttenberg 9 June 2015)
No tessellation as such,
mostly of ornament in various forms.
Dudeney, Henry Ernest (edited by Martin Gardner). 536
Puzzles & Curious Problems. Souvenir Press London.1968 (7 June 1997)
and second edition 1919 (26 August 2001)
An absolute classic in the
field, but no tessellation as such! Dissection puzzles pp. 114-125.
————. Amusements in Mathematics. Thomas Nelson and
Sons Ltd. 1947 (5 February 1994) and Dover Publications, Inc. 1958, 1970 (11
September 2000). First published in 1917. Numerous reprints.
Loosely 15 chapters, with in
particular of interest a chapter on ‘Geometrical Problems’, pp. 27-55, with
Dissection Puzzles, Greek Cross Various Dissection Puzzles, Patchwork Puzzles
and Various Geometrical Puzzles. The book is full of interest; however, there
is no tessellation whatsoever!
————. A Puzzle-Mine. Subtitled ‘Puzzles Collected
From The Works Of The Late Henry Ernest Dudeney’, by J. Travers. Thomas Nelson
and Sons Ltd. Date of publication surprisingly not stated. However, Frederickson
gives this as 1931. (11 October 1997)
An editorial note states that
the puzzles in this book were originally published in serial form in the
magazine Blighty and after the war of
Four chapters of classic
Dudeney fayre. Although all of interest, of most note is Chapter III, dissection puzzles, pp. 81-85. Likely these
repeat others in his books. As ever, no tessellation as such.
————. (Edited by Martin Gardner) plus Puzzles and Curious Problems.
More than 250 tantalising brain teasers
by the puzzle king. Collins Fontana Books. Small format paperback. (19 July
Essentially the same as
immediately below, with ‘more’ added to the title, and the same contents,
although of a three-page increase, the reason of which I refrain from
————. (Edited by Martin Gardner) Puzzles and Curious
Problems. More than 250 tantalising
brain teasers by the puzzle king. Small format paperback. Collins Fontana
Books 1970. First published in Great
Britain by Souvenir Press (qv) under the
title ‘536 Puzzles and Curious Problems’. (8 August 1993)
This is the first part, of 258
puzzles, with answers (I do not have the second part). Oddly, within the same
contents framework, and so would appear that the books are the ‘same’, the
puzzles are different, and bear no direct correlation to each other!
————. The Canterbury
Puzzles. Thomas Nelson and Sons, Ltd. Second Edition 1919 Fourth edition
1932 (with some fuller solutions and additional notes). (16 November 1996)
114 puzzles in nine chapters,
with solutions. Occasional references to tiling and dissections: 19, The Puzzle
of the Prioress asymmetric cross to square; 26, ‘The Haberdasher’s Puzzle’,
dissection, triangle to square; 37, ‘The Crescent and the Cross’ (on
dissection), 77 ‘Making a Flag’; 84 ‘The Japanese Ladies and the Carpet’, and
of course much else of interest in a generalised sense.
Dye, Daniel Sheets. The New Book of Chinese Lattice
Designs. 372 Designs. Dover Publications Inc, New York 1981 (first published). Edited and
with an introduction by Nancy Balderston Conrad (9 April 1993)
The introduction states that
these are designs that were not included in his earlier book Chinese Lattice Designs. The book is diagram
heavy and text light (only the barest of descriptions are given for classifications),
of which the later is sorely missed; these are crying out for background
details. I considerer this book to be very much the poor relation to the other.
Balderston, mentioned in the dedication, is a relative of Dye in some way. His
wife has Balderston as her middle name.
Cairo tilings. Of occasional interest: p. 69, with a par hexagon divided into
unequal kites, with a secondary feature of squares or vice versa. P. 103, of a
curious two-tile tiling of a common arc of an underlying square tessellation
worthy of study.
————. Chinese Lattice Designs. 1200 Designs. Dover
Publications Inc, New York
1981. (9 April 1993)
This apparently first appeared
in 1937 titled as A Grammar of Chinese
Lattice. Checked entire book for Cairo
type tilings May 2011. Only ‘faux’ instance is of p. 340, a Greek cross with a ‘x’
in centre. Page 420 has a Chinese parquet likeness source from Gardner’s 1983 article.
above is stated by Peter Hilton and Jean
Pederson of a reprint of A Grammar of
Chinese Lattice Harvard-Yenching
Institute Monograph Series, Vol .VI, Harvard University Press, Cambridge, Mass,
Eastaway, Robert, editor. Enigmas. The World’s Most
Puzzling Book. Arlington
Books (Publishers) Ltd 1982. (31 October 1993). First saw in Scartho library 21
December 1987, or at least the first recorded study.
A compilation from the pages
of New Scientist’s weekly Enigma
column, described as ‘… 69 brain-teasers…’, in nine sections. The style is
Gardneresque. Curiously, it would appear from the acknowledgements that
Eastaway had nothing to do with the puzzles per se! The puzzles are mostly in the form of ‘stories’, rather than of
abstract mathematical problems. Of most interest is ‘Shapes and Sizes’, pp.
83-90 of six geometrical figures. The first, ‘grid halving’, on geometrical
dissections, of cutting a figure into two equal parts, was the only one
‘studied’. Another dissection problem, ‘Two-Square Dissection’ was not studied.
Note that there are no tessellation problems. As such, a minor, inconsequential
study was made.
Eastaway, Rob and John Haigh. How to take a Penalty. The Hidden Mathematics of Sport Robson
books, an imprint of Chrysalis books group PLC
(6 August 2011)
Eckler, Ross. Making
the Alphabet Dance. Recreational Wordplay. Macmillan 2001. First published
1997. (21 February 2015)
Chance finding. Although out
of my direct interest, with many notables named here, such as Martin Gardner,
it was judged worth a look. I must say that I am surprised that the book’s
author, Ross Eckler, and indeed the book itself, first published in 1997, had
escaped my orbit.
Edwards, Cyril and Phil Boorman. Geometry. Macdonald
Educational Colour Units 1976 (5 June 1994 and c.2000?)
Do I have two copies? note
that although this is a book in its own right, it is also part on a series of
Mathematics by the Macdonald Educational, Colour Units with other titles: Sets and Religion, Trigonometry, Statistics*,
Number and Patterns, Groups and Finite Arithmetic*, Matrices, Calculating Aids, Vectors,
Graphset Algebra. * In possession. Statistics is by Lynn Jones. The level is
fairly basic (and of relatively few pages, just 24), with simple geometric
constructions. Although there is some advanced maths here and there, the tenure
is one of for beginners. Save for one instance, more or less in passing on page
24, there is no tiling here.
Edwards, Cyril. Groups
and Finite Arithmetic. Macdonald Educational Colour Units 1974 (12 November
Although of repeat patterns
and symmetry there is nothing of any real interest.
Elffers, Joost. Translated by R. J. Hollingdale. Tangram.
The Ancient Chinese Shapes Game First published Verlag M. Dumont
Schauberg 1973 (19 May 1995). Penguin Books 1984.
Small format paperback, c. 200
pp. Perhaps more of a samarbeid que
the single author given suggests, with a Introduction (Jost Elffers with Erik
van Grieken). History (by Jan van der Waals) pp. 9-27, and bibliography by (Jan
van der Waals), pp. 29-31 pp. 123-124, an essay ‘Counting and Classifying
Tangrams’ (by Michel Dekking with Jaap Goudsmit). Gives a most interesting and
useful tangram history. Then gives a series of tangram diagrams without further
commentary. Of general geometrical interest, nothing more. Quite what the background of Elffers is went
Elffers, Joost and Michael Schuyt. Tangram. ils
Ancient Chinese Shape Game. Barnes & Noble Books 2001 (26 April 2010).
A boxed set of tangrams and
Elliot, Marion. The Tile Decorating Book.
Lorenz Books 1997. (19 October 2008)
El-Said, Issam; Ayse Parman. Geometric Concepts in
Islamic Art. World of Islam Festival Publishing Company Ltd. 1976 (2009)
Many references to ‘tomb
towers’ re Carol Biers’ interest.
Engel, Peter. Origami: from Angelfish to Zen. Dover
Publications Inc. 1989 (26 May 2008).
reference to Escher’s tessellations and prints, pp. 2-5, 69. Cover has an
adapted ‘Drawing Hands’, in relation to the origami premise of the book.
Ernst, Bruno. The Magic Mirror of M. C. Escher.
Tarquin Publications 1985 (first published 1972. (19 August 1988) First saw in 1987,
and ordered 19 August 1988
A major work on Escher, one of
the ‘core value’ books; Indispensable! However, of note is just how little tessellation there is! The book is primarily on spatial structures. And what
little there is, this is subsumed by the above premise.
————. Adventures with Impossible Figures. Tarquin
Publications 1986. (9 April 1993)
————. The Eye Beguiled. Optical Illusions. Benedikt
Taschen 1992 (10 August 1993)
Although not strictly a
tessellation book, included here as there is a certain amount of crossover. plus
of impossible objects, Ernst’s forte, rather than a generic optical illusion
book. Has a scholarly bibliography. Escher prints Concave and Convex s. 27, Belvedere p. 77. Small section on Escher
per se, pp. 74-80. Escher Belvedere model by Shigeo Fukada pp. 92-93.
Escher, M. C. Grafiek
en tekeningen M. C. Escher. Contribution by P. Terpstra. Zwolle: J. J. Tijl, 1960 (first printing
1959). (21 October 2016)
Gift of Peter Raedschelders. en
Dutch. One of the core value, ‘must have’ books on Escher. In brief, an
eclectic selection of 39 of his works (later expanded to 76 in a subsequent
edition), divided into nine (and later 10) classifications. Shows 13 plane
tilings. Each entry is accompanied by a brief commentary, albeit in Dutch, of
which I discuss this is the English translation.
Of note here is P. Terpstra’s
essay, pp.11-13, ‘Its over de wiskundige achtergrond van regelamatige
vlakverdelingen’ not shown in subsequent editions. Also has a catalogue not in subsequent
Escher, M. C. The Graphic Work of M. C. Escher.
1970. (8 August 2004) and Taschen (10 August 1993) (First saw in September
1987, Louth library)
One of the core value, ‘must
have’ books on Escher. Expanded edition of the 1960 first published. In brief,
an eclectic selection of 76 of his works, divided into ten classifications: 1.
Early prints, 2. Regular division of a plane, 3. Unlimited spaces, 4. Spatial
rings and spirals 5. Mirror images, 6. Inversion, 7. Polyhedrons 8.
Relativities, 9. Conflict flat-spatial and 10. Impossible buildings. Each entry
is accompanied by a brief commentary, albeit this is generally lightweight, and
de which shows little new insight.
————. M. C. Escher 29 Master Prints. Harry N.
Abrams, Inc. Publishers New York
1983. Edited by Darlene Geis. First saw 18 July 1992. (9 April
Very large format book, 64 pp.
In addition to the 29 Master Prints (by and large a fair description, given the inclusion of
Day and Night and Sky and Water I, although no Verbum), both tessellation and
others, the book includes an essay by Escher, 'On Being a Graphic Artist' and with commentaries on the prints,
mostly by Escher, and additionally, in most a most minor way, by C. H. A. Broos,
J. L. Locher, Bruno Ernst and H. S. M. Coxeter. However, none of this text
appears to be original; it appearing in other sources, as according to the
to a reference on an old ring (cardboard) binder cover, I first saw this in
Grimsby central library on 18 July 1992,
but have since completely forgotten about this! Whether this was as on the
shelves or was ordered I do not recall. Whatever, it was not significant in
that no new studies arose from this.
Espy, Willard R. The Game of Words. Wolfe Publishing
Ltd. 1971 (two books, one obviously forgotten upon purchasing, one book not
dated, one 7 June 1997)
Although not strictly
mathematical per se, being of word play, of interest to the mathematical mind,
and so hence included here.
Falletta, Nicholas. ils
Paradoxicon. A Collection of
Contradictory Challenges Problematical Puzzles and Impossible Illustrations.
Turnstone Press 1985 (29 November 1992). First published by Doubleday and
Company, New York, 1983. First saw (or at least studied) 15 September 1987, Scartho,
The 1983 edition has a front
cover picture (among others) of Escher’s Drawing
Hands. Has much of interest in a generalised sense, albeit some I have no
interest in. However, it is more of a compilation nature, rather than of
original research. Many references to Escher, notably with a dedicated chapter,
‘M. C. Escher’s Paradoxes’ pp. 24-34, and illustrations throughout; pp. 54,
98-99, 101, 157, 190. Other chapters of note not pertaining to Escher include
‘Geometric Vanishes’, pp. 35-40.
Falkener, Edward. Games Ancient And Oriental And How To
Play Them. Dover Publications, Inc., New
Farnworth, Warren. Techniques
and Designs in Pin and Thread Craft. B T Batsford Ltd, London 1977. First
saw c. 23 June 1987. (26 April 1998)
Although not strictly on
mathematics, included as it was studied among my early’ mathematical’ studies
Farrell, Margaret A. (ed). Imaginative Ideas for the Teacher of Mathematics, Grades K-12.
Ranucci’s Reservoir. National Council of Teachers of Mathematics (NCTM)
1988 (30 April 1994)
A compilation by Farrell of 21
articles, in five parts, of Ernest Ranucci’s works. Of most interest is Part 4:
Inventiveness in Geometry, with tessellation articles: ‘A Tiny Treasury of
Tessellations’ and ‘Master of Tessellations: M. C. Escher, 1998-1972’.
Such a ‘type’ of book was more
interest in the ‘old days’ (pre-internet), where easy access to published
journals was not widely available. The book also contains an excellent
bibliography of his works and biography. Of the two papers, of note is that the
Cairo-esque diagram. I had though that this was unique to his book Tessellation and Dissection.
Has Fish and Scales on front cover.
Fathauer, Robert. Designing and Drawing Tessellations.
No publisher given. 2008 (18 July 2009)
I consider the title a little
misleading, given that the premise is one of creating Escher-like tessellation, rather than non-lifelike tessellation per
se as the title would otherwise suggest. One of the few books to approach the
topic in depth, and so is warmly welcomed. Chapter 1 gives a history and among
various matter discusses pavement tessellations, and mentions the Cairo tiling.
Fellows, Miranda. ils
Life and Works of Escher. Parragon Book Service Limited, 1995 (14 May 2016)
Small format hardback. Fellows
comments on a selection of Escher’s works. Seen (where is long forgotten) many
years ago, but (I think) judged so lightweight as to not worthy of pursuing,
perhaps a little unfairly in retrospect.
Does not have a Escher
bibliography, as might have been thought.
Fenn, Amor. Abstract
Design and How to Create It. Dover Publications Inc 1993. Republication of
the original of 1930, with a new introduction by Richard M. Proctor (21
The premise is of design, with
stripes, wall papers, rather than tessellation per se. This is very much as in
the style of another book of the time, Pattern
Design, by Lewis F. Day. Houndstooth tiling p. 129, albeit nor sourced in
the text. Nothing particularly innovative here, certainly as regards
Feravolo, Rocco. Wonders of Mathematics. A Wheaton
& Co. Ltd. 1964 (not dated, c.10 years ago)
Ferris, Timothy (ed.) The World Treasury of Physics,
Astronomy, and Mathematics. Little, Brown and Company 1991. (3 September
1998?; The last digit has faded).
Anthologies by sixty leading
authors; G.H Hardy, Benoit Mandelbrot etc. (Mathematics, Chapter 4).
Nancy Eckert, Ann Fetter, Doris Schattschneider, Cindy Schmalzried, Eugene
Klotz. The Platonic Solids Activity Book. Backline Masters. Key
Curriculum Press, Berkeley, CA. 1991 (30 April 1994)
Cairo reference and line drawing page 21, and repeated page 96,
the reason for this being teachers and student questions. The quotation repeats
Scientific American assertion re ‘ … seen in Moorish buildings…’ (and is likely
taken from that reference; Schattschneider’s contribution?). Minor Escher-like
art, a bird, page 20.
Also see companion book ils Stella
Octangula Activity Book, Hilary Brest et al.
Field, Michael and Martin
Golubitsky. Symmetry in Chaos. A Search
for Pattern in Mathematics, Art and Nature. Oxford University Press 1992.
Decidedly advanced, very
little of which is accessible to me. Mostly of pattern using advanced equations
rather than tiling. Escher's Horsemen p. 59.
Field, J. V. Kepler's Geometrical Cosmology. The University of Chicago Press, 1988. (19 November 1994)
Also see her article on
‘Kepler’s star polyhedra’.
Field, June. Creative
Patchwork. Pan Books 1976. First edition 1974 by Sir Isaac Pitman and Sons
Ltd. (30 September 2000)
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has crossovers,
However, now, and for some considerable time, the nature of the material is considered
hardly worthy the time originally devoted to it. as such, I seem to recall this
book from my 1987 studies, although there is no documented connection.
Mazes Ancient & Modern. Tarquin Publications 2001. (Date not stated)
————. Geometric Patterns from Roman Mosaics and how to
draw them. Tarquin Publications 1988. (3 June 1993)
Small booklet, 64 pages. note
that Field has a like format five-book series with the title ‘Geometric
Patterns’, with a variation. Tiles and Brickwork, Islamic Art and Architecture,
Churches & Cathedrals, From Patchwork Quilts, and one outlier, Mazes
Ancient & Modern. No Cairo
Fletcher, David and Joseph Ibbotson. Geometry Two.
Holmes McDougall Limited 1967 (25 October 1998 year is semi legible)
Pitched at a 8-12-year-age
level. Note that this is a three-book series, of which I only have book 2. Tilings
pp. 20-21, but only of the most simplest investigation of the ‘angle proof’.
Gives ‘new’ means of drawing octagons, p. 44.
Fletcher, Harold. Mathematics for Schools. Teacher’s
Research Book. Level II Books 1 and 2.
Addison–Wesley Publishers Limited 1971 (3 September 2006).
Juvenile. No real interest,
primary maths. Symmetry pp. 50-54, no tessellation.
Fletcher, Alan. ils
art of looking sideways (Sic). Phaidon. No bibliography detail! (Grimsby library, 5 May
2012, although seen many years ago)
Although not a maths book per
se, included as it has a few pages on tilings, notably p. 255 and next three
pages – pages are not ‘truly’ numbered here! Although the book is indeed light
on tiling, the tilings it does contain are of significance, containing new material.
These are taken from a page in matematisk
Models, page 64, itself taken from an earlier source, Daily Telegraph in 1955 (the exact issue is uncertain, regrettably,
no other details are given, and so have not been able to obtain). Fletcher
apparently builds on this, with further tiling. I say apparently, perhaps these first appeared in the Telegraph? He
credits the Telegraph article.
Ford, Karin (translator) and Janet Wilson, editor. Anglais
Language version. Escher on Escher. Exploring the Infinite. Harry N.
Abrams, Inc. 1989. (29 May 1991). With a contribution by J. W. Vermeulen.
Compiled by W. J. van Hoorn and F. Wierda. Originally published under the title
Small format paperback. A series
of translated essays of Escher's own writings and previously unpublished
speeches in Dutch, and so warmly welcomed. Ceux-ci comprennent:
1. Newsletter of the Dutch Circle of Graphic Artists and Illustrators,
Non. 5, December, 1950. The Craft. 10-12. Dear Oey…
2. Newsletter of the Dutch Circle of Graphic Artists and Illustrators,
Non. 3, June, 1950. Our Brother 13-15. Dear Oey…
3. De Grafische (The Graphic Arts), No. 13, September, 1951.
4. Acceptance Speech by M. C.
Escher upon receiving the Culture Prize of the City of Hilversum on March 5,
5. Prepared lecture for
Lexington, Massachusetts, US not given by Escher due to ill health – The Regular
Division of the Plane 24-53 (part 1); Other Themes 54-80 (part 2)
6. How Did You as a Graphic
Designer Come to Make Designs for Wall Decorations? De Delver (the Digger), xiv, No. 6, 1941 83-88
7. The Regular Division of the Plane 90-122 (also published in M. C.
Escher The Complete Graphic Work)
8. Approaches to Infinity (no
context or date given). 123-127 (as given in Locher)
9. Perspective (no context or
date given). 128-134
10. The Impossible (no context
or date given). 135-136
11. I’m Walking All Round All By Myself Here, by J. W. Vermeulen 139-153.
A portrait of Escher, by his accountant.
A notable aid in Escher
scholarship, with numerous Dutch texts made readily available. Has a ‘serious’
bibliography, p. 154, albeit brief, under the title ‘selected bibliography’.
This is best described as partial, taken from ?
Forty, S. M C Escher. Taj Books 2003 (11 October
Oversize. The premise is of a
‘grand picture book’ per se, with 74 works, of prints (mostly) and drawings. Der
does not appear to be any new research, with the brief introductory text
apparently assembled from existing sources. Shortcomings and faults abound
here. Ideally each print or drawing would be accompanied with some text;
however there is no individual commentary whatsoever, a major shortcoming.
There is no formal introduction per se. The text that serves for the
introduction, pp. 5-11, as ‘Maurits Cornelis Escher 1898-1972’ is of an overall
guide. However this is riddled with errors, of basic English and story. Apostrophes
are used both incorrectly and correctly, with ‘the Escher's first…’ p. 7 and
‘the Eschers’. Also apostrophes are omitted (purposefully?) in the plates 1, 7,
yet are used correctly elsewhere, plates 44, 59. Such slapdash work is
inexcusable, given that (a) the author is a graduate of London University, and
so should know better, and (b) the text, of just seven pages is hardly of such
a length that it would be overlooked as would a piece in say a 300-page work feasibly
would. Some text is just plain wrong: ‘failed all his exams except mathematics’’.
At high school in Arnhem, I was extremely poor at
arithmetic and algebra because I had, and still have, great difficulty with the
abstractions of numbers and letters. When, later, in stereometry (solid
geometry), an appeal was made to my imagination, it went a bit better, but in
school I never excelled in that subject. But our path through life can take strange
Other statements need checking
for veracity. Given the above shortcomings and errors I am not sure how much
the text can be relied on, but I lack the time to investigate as I would like. Useful
for seeing Escher’s prints at a larger size than in most books, but not much
more. No bibliography, although the nature of the book does not lead to this.
Foster, Leslie. Rainbow Mathematics Encyclopedia.
Grisewood & Dempsey Ltd. 1985 W.H. Smith edition (19 March 2005)
Foster, Richard. Patterns of Thought. The hidden meaning
of the great pavement of Westminster
abbey. Jonathan Cape, London 1991 (12 February 1994, York)
A general account of the
pavement. Chapter 6, pp. 111-130 concerns the aspect most of interest, from a
geometrician point of view.
E. Curiosités Géométriques. Paris
1907 (downloaded from internet archive 28 April 2015).
From a reference in Bradley. A little disappointing,
in that tiling is only mentioned briefly pp. 363-371 on the PDF numbering.
————. Recreations Mathématiques. Paris 1899
From a reference in MacMahon. Strictly nombre recreations, of which although of
interest again disappointing, as I was hoping for tiling.
Franke, Herbert W. Computer Graphics Computer Art. Phaidon,
1971. Other, later editions of 1985. Originally published as Computergraphik-Computerkunst (First saw
November 1987?) (30 December 2016)
for foreseen forthcoming review purposes, having previously last studied in November
1987. As such, I only had dim and distant memories of this book, having last
seen it nearly 30 years ago! Indeed, I couldn’t really picture or remember the
contents. Be all that as it may, the book has next to no connection with
tessellation. Indeed, there is not a single instance! As such, a useful guide
to computer graphics of the day, but now a little dated, but still of interest
as to historical matters. Has an excellent biography and bibliography sections,
albeit I simply do not have the time to pursue these, as much as I would like
My brief studies of this, of just four sheets, are
dated 23 November and 2 December 1987, of
s. 96. Pages of interest include, frontispiece, of a dragon space-filing
curve, p.18, 30, of a metamorphosis, of a loose parquet deformation nature; op
art by A. Michael Noll, p. 67.
Francis, Daryl. Puzzles
& Teasers for Everyone. Paperfronts. Elliot Right Way Books c. 1980 (10
Freaker, Daniel and Alan Parsons. Series consultant Harry
Smith. Revise BTEC National Art and
Design. Revision Guide. Pearson 2018. (19 June 2018)
For 11-16 age children. Features my bird and fish
tessellation, p. 85. The text is Freaker and Parsons' own, of qui I do not fullstendig agree with .
Freeman, Mae and Ira Freeman. Fun with Geometry. Kaye
& Ward, London
1969. First published in 1958 (24 October 1998)
28 different two-page essays
on ‘popular geometry’ both ‘theoretical’ and ‘applied’, aimed at a juvenile
audience. That said, some aspects are new to me here! Measuring distances, pp.
24-25 and the three tags, pp. 50-51. Much of this is Gardneresque nature,
albeit pitched at youth. Geometric dissections pp. 52-53, but no tiling as
Freese, Ernest Irving. Perspective
Projection: A Simple and Exact Method of Making Perspective Drawings. New
York Pecil Points Press, 1930 (15 March 2018)
From a link on Greg
Frederickson’s update page, viewed (but not downloaded) at The Hathi Trust. qui
the title suggests, on perspective, with no foreshadowing of his work in
geometric dissections, or anything on tiling per se.
Frederickson, Greg N. Dissections: Plane & Fancy.
Cambridge University Press 1997. (28 February
An absolute delight! Highlight
after highlight, too many to list here, although I am merely an ‘interested
bystander’ in the field. 24 chapters and an excellent bibliography. Speculations
as to who ‘A. E. Hill’ was, pp. 157-158, 290-291. Has many interesting brief
biographies of the main people in the field, past and present, including
Dudeney, p. 81. à
me at least, and I suspect most other people, this is the more important of his
three books on the theme, the other two, Hinged
et Piano-Hinged Dissections are more
of a specialised nature.
————. Hinged Dissections: Swinging & Twisting. Cambridge University Press. 2002 (?)
Perhaps somewhat out of
mainstream interest, of a specialised branch of dissections. Nonetheless, it
remains full of interest. Has asides in the form of ‘Curious Case’ and
‘Turnabout’, with much on Dudeney.
————. Piano-Hinged Dissections: Time to Fold. A. K. Peters,
Ltd. 2006. Not date stamped. A receipt states ‘processed September 9 2008’
gives indication as to obtaining.
Perhaps somewhat out of
mainstream interest, of a specialised branch of dissections. Nonetheless full
of interest. Has asides in the form of Ernest Irving Freese’s lost manuscript
and ‘Folderol’ (of which such term I was unfamiliar with; the dictionary gives
it ‘anything trifling’).
————. Ernest Irving
Freese's Geometric Transformations: The Man, The Manuscript, the Magnificent
Dissections! World Scientific 2018
(2 February 2018)
At last, after no less than 60
years, Freese’s work is shown in its entirety!
————. ‘Hugo Hadwiger’s influence on geometric dissections with
special properties’. Elemente der
Mathematik. 65 (2010) 154 –164 (2 September 2016)
Freebury, H. A. A History
of Mathematics. For Secondary Schools. Cassell & Co. Ltd. 1958 (8 July
French, P. Introducing Polyhedra. McGraw-Hill
Publishing Company Limited 1966. First published 1964 by the House of Grant. (24
Slim volume paperback, 39 pp. Juvenile,
Junior, 8-11 years. Part of the 13-book series on the title ‘Exploring
Mathematics’, by P. French and R. J. Rickard, under the generell editor J. B.
Palframan. Gives compass construction nets and brief history. although not explicitly stated for children, it is clear that this is the indeed the intended
audience. Too simplistic to be of any use.
Friedhoff, Richard Mark and William Benzon. Visualization.
The second computer revolution W. H. Freeman and Company New York 1991. (11 September 1994)
A pleasing read, largely accessible,
although there is only subsidiary discussions on related mathematical aspects,
such as fractals. No tessellation, no Escher.
Frisby, John P. Seeing.
Illusion, Brain and Mind. Oxford University Press, 1979. First saw 1987.
(13 February 2017)
Although a book on seeing in
the broad context and so not on maths, it is included in this listing as it features
Escher’s ‘seeing-related’ prints (tessellation is not mentioned), as well of
interest in a variety of ways in a generalised sense. Upon the ongoing (2017)
review process of all 1987 studies, specially purchased. Although ostensibly of
a popular nature, the text nonetheless remains is in general of a forbidding
nature. Features two of Escher’s prints in Chapter 1 ‘Pictures in our Heads’, pp.
22-23, Ascending and Descending et Waterfall. However, there is only minor
commentary, p. 19. However, one pleasing nuance is that Frisby astutely
observes the fine distinction of ‘Monk’s work’ in the discussion of Ascending and Descending qui ubrukelig labour of which most other
commentators do not, missing the ‘useless’ point.
Further to the book, I happened
to notice on the dust jacket the following intriguing quote:
One of his special interests is in the art of M. C.
Upon following up with him
(mail, February 2017), he told me:
… When I published the first edition of Seeing the publishers
suddenly sprang on me a request for ‘special interests’ and in a bit of a rush
I mentioned Escher whose work at that time (around 1978-79) I was using to
illustrate some lectures. In fact, while an admirer, I have no deep interest in
Therefore, it wasn’t a ‘special
interest’ after all, but rather just a passing interest! But at least I know
Fuller, Buckminster R. Utopia or Oblivion. The Prospects for Humanity. Penguin
Books 1972 (20 September 1992). First published in the USA 1969
Small format paperback, 416
pp. Text heavy. The cover has sfære
packing diagrams, which my have attracted my attention. I simply don’t have the
time to read this. It may come in useful for reference purposes. Chapter 3,
Prevailing Conditions in the Arts’, on geometry, is the only aspect of direct interest. Je
read somewhere (Coxeter?) that Fuller was somewhat crankish (or overstated) in
many ways. Whatever, the book was never studied per se.
Gale, Howard et al. ils
Times Tournament of the Mind. Times Books Limited 1988. (not dated, c 10
Gardiner, Anthony. matematisk
Puzzling. Oxford University Press 1987 (15 September 1989)
Popular account from an
academic, 153 pp. Not in possession, saw at Grant Thorald library on 15 September
1989 and made a minor study of that date on a shared paper of A. Racinet and
Michele Byam of 10 and 17 January 1989 henholdsvis. The book has long been deleted from stock, and ideally I would obtain
again, if only to aid in a review. However, even of the lowest price on Amazon
I am not planning on doing so. Pages studied 49, of circle packing and 73, of
indeterminate means. Gardiner is a notable mathematician, with 15 books to his
nom; possibly this was the first.
See Chapter 11, ‘Circles and
Spheres’, pp. 49-51. and Chapter 16 Polygons, pp. 71-74. selv om ostensibly Chapter
11 is on circle packing, this is not so, or at least as seen at first
impression such a fitting circles into a square. Rather the premise is of fitting
the largest circles inside the central part hole of each konfigurasjon.
Gardner, Martin. 1. Mathematical Puzzles and Diversions.
Penguin Books (original edition 1959). (30 August 1993). Also London G. Bell and Sons Limited 1963.
Hardback (19 November 1994) and Pelican (30 August 1993)
First, regarding the listing
of columns in Gardner’s compilations in books below, the entries in bold are of
extra special renter, primarily of tiling matters, although drawing hard and
fast lines is an invidious task at times. Quite simply his collection is
indispensable! Les propriétaires étaient irriterendeet infuriatingly, these do not always reflektere the original title and so correlating like articles is not a rett fram task as it may otherwise appear to be. As a preamble to Gardner’s collection of
columns over 25 years in 15 books, these are a fresh delight time and again, as
due to such an extensive compilation one simply forgets, save for core value
articles! Further to the core values, for each book, where appropriate I list
such instances, primarily involving tessellation and/or Escher aspects,
although at times there is no firm boundary. For each book I list each chapter,
although these do not always tally with the original article in Scientifiquement américain (a bone of contention).
1 Hexaflexagons, 2 Magic with
a Matrix, 3 Nine Problems, 4 Ticktacktoe, or Noughts and Crosses, 5 Probability
Paradoxes, 6 The Icosian Game and the Tower of Hanoi, 7 Curious Topological
Models, 8 The Game of Hex, 9 Sam Loyd: America’s Greatest Puzzlist, 10
Mathematical Card Tricks, 11 Memorizing Numbers, 12 Nine More Problems, 13
Polyominoes, 14 Fallacies, 15 Nim and Tac Tix, 16 Left or Right? References for
————. 2. More Mathematical Puzzles and Diversions.
Penguin Books 1966. First edition 1962 (19 November 1994)
1 The Five
Platonic Solids, 2 Tetraflexagons, 3
Henry Ernest Dudeney: England’s Greatest
Puzzlist, 4 Digital Roots, 5 Nine Problems, 6 The Soma Cube, 7 Recreational
Topology, 8 Phi: The Golden Ratio, 9 The Monkey and the Coconuts, 10 Mazes, 11 Recreational
Logic, 12 Magic Squares, 13 James Hugh Riley Shows, Inc., 14 Nine More
Problems, 15 Eleusis: The Induction Game, 16 Origami, 17 Squaring the Square 18
Mechanical Puzzles, 19 Probability and Ambiguity, 20 References for Further
Of note is the
Dudeney reference, of June 1958.
————. 3. New
Mathematical Diversions from Scientific American (1966) London George Allen and Unwin Ltd., 1969 (12
(Full title is Martin Gardner’s New Mathematical Diversions
from Scientific American; cover and title page differ)
1 The Binary System, 2 Group
Theory and Braids, 3 Eight Problems, 4 The Games and Puzzles of Lewis Carroll,
5 Paper Cutting, 6 Board Games, 7 Packing Spheres, 8 The Transcendental Number
Pi, 9 Victor Eigen: Mathemagician, 10 The Four-Color Map Problem, 11 Mr.
Apollinax Visits New York, 12 Nine Problems, 13 Polyominoes and Fault-Free
Rectangles, 14 Euler’s Spoilers: The Discovery of an Order-10 Graeco-Latin
Square, 15 The Ellipse, 16 The 24 Color Squares and the 30 Color Cubes, 17 H.S.M. Coxeter, 18 Bridg-it and
Other Games, 19 Nine More Problems, 20 The Calculus of Finite Differences
Of core interest: 17 H.S.M.
Coxeter, with use of Escher's works: Horseman, Two Birds, Verbum
————. 4. ils
Numerology of Dr. Matrix (columns 1-7, 1967; expanded 1976 with columns
8-18 as The Incredible Dr. Matrix;
expanded 1985 with columns 19-22 as ils
Magic Numbers of Dr. Matrix) Charles Scribner’s and Sons, 1976 (7 November
1 New York, 2 Los Angeles, 3
Sing Sing, 4 Lincoln and Kennedy, 5 Chicago, 6 Miami Beach, 7 Philadelphia, 8
Pi, 9 Wordsmith College, 10 Squaresville, 11 Left Versus Right, 13 Fifth
Avenue, 14 The Moon, 15 Honolulu, 16 Houston, 17 Clairvoyance Test, 18 Pyramid
Lake, (and later, 1985 edition) 19 The King James Bible, 20 Calcutta, 21
Stanford, 22 Chautauqua, 23 Istanbul, Answers and Commentary
All on numerology; a major
disappointment! I was forventer other articles with the Dr Matrix kolonner, as
with other books in which an initial
title is insinuated. I have the second edition, The Incredible Dr. Matrix.
————. 5. ils
Unexpected Hanging and Other Mathematical Diversions. (1969; UK Further
Mathematical Diversions) Simon and Shuster 1969 (14 June
1 The Paradox of
the Unexpected Hanging, 2 Knots and Borromean Rings, 3 The Transcendental
Number e, 4 Geometric Dissections, 5 Scarne on Gambling, 6 The Church of the
Fourth Dimension, 7 Eight Problems, 8 A Matchbox Game-Learning Machine, 9
Spirals, 10 Rotations and Reflections, 11 Peg Solitaire, 12 Flatlands, 13
Chicago Magic Conventions, 14 Tests of Divisibility, 15 Nine Problems, 16 The
Eight Queens and Other Chessboard Diversions, 17 A Loop of String, 18 Curves of
Constant Width, 19 Rep-Tiles:
Replicating Figures on the Plane, 20 Thirty-Seven Catch Questions,
Of most interest: Geometric
Dissections, pp. 43-51 and Rep-tiles Replicating Figures on the Plane, pp.
————. 6. Martin
Gardner's Sixth Book of Mathematical Diversions from Scientific American (W.
H. Freeman and Co, 1971) (24 December 2011)
1 The Helix, 2 Klein Bottles
and Other Surfaces, 3 Combinatorial Theory, 4 Bouncing Balls in Polygons and
Polyhedrons, 5 Four Unusual Board Games, 6 The Rigid Square and Eight Other
Problems, 7 Sliding-Block Puzzles, 8 Parity Checks, 9 Patterns and Primes, 10
Graph Theory, 11 The Ternary System, 12 The Trip around the Moon and Seven
Other Problems, 13 The Cycloid: Helen of Geometry, 14 Mathematical Magic Trick,
15 Word Play, 16 The Pythagorean Theorem, 17 Limits of Infinite Series, 18
Polyiamonds, 19 Tetrahedrons, 20 Coleridge's Apples and Eight Other Problems,
21 The Lattice of Integers, 22 Infinite Regress, 23 O'Gara, the Mathematical
Mailman, 24 Op Art, 25 Extraterrestrial Communication
22 Infinite Regress has Escher’s
‘Drawing Hands’ print p. 224, and is mentioned in passing, p. 223
————. 7. Mathematical Carnival. Pelican
Books (1977) 1978. (Undated c. late 1990?) Hardback
1 Sprouts and Brussels
Sprouts, 2 Penny Puzzles, 3 Aleph-Null and Aleph-One, 4 Hypercubes, 5 Magic
Stars and Polyhedrons, 6 Calculating Prodigies, 7 Tricks of Lightning
Calculators, 8 The Art of M.C. Escher,
9 The Red-Faced Cube and Other Problems, 10 Card Shuffles, 11 Mrs Perkins'
Quilt and Other Square-Packing Problems, 12 The Numerology of Dr. Fliess, 13
Random Numbers, 14 The Rising Hourglass and Other Physics Puzzles, 15 Pascal's
Triangle, 16 Jam, Hot and Other Games, 17 Cooks and Quibble-Cooks, 18 Piet
Hein's Superellipse, 19 How to Trisect an Angle, Bibliography
————. 8. matematisk
Magic Show. Viking (1977)
1984 (26 May 2001)
1 Nothing, 2
More Ado About Nothing, 3 Game Theory, Guess It, Foxholes, 4 Factorial
Oddities, 5 The Cocktail Cherry and Other Problems, 6 Double Acrostics, 7
Playing Cards, 8 Finger Arithmetic, 9 Möbius Bands, 10 Ridiculous Questions, 11
Polyhexes and Polyaboloes, 12 Perfect, Amicable, Sociable, 13 Polyominoes and
Rectification, 14 Knights of the Square Table, 15 The Dragon Curve and Other
Problems, 16 Colored Triangles and Cubes,
17 Trees, 18 Dice, 19 Everything, Bibliography
16 is on MacMahon.
————. 9. Mathematical Circus. Optical illusions!
Games, puzzles, paradoxes. (1979) Hardback (23 December 1995)
Illusions, 2 Matches, 3 Spheres and Hyperspheres, 4 Patterns of Induction, 5
Elegant Triangles, 6 Random Walks and Gambling, 7 Random Walks on the Plane and
in Space, 8 Boolean Algebra, 9 Can Machines Think?, 10 Cyclic Numbers, 11
Eccentric Chess and Other Problems, 12 Dominoes, 13 Fibonacci and Lucas
Numbers, 14 Simplicity, 15 The Rotating Round Table and Other Problems, 16
Solar System Oddities, 17 Mascheroni Constructions, 18 The Abacus, 19
Palindromes: Words and Numbers, 20 Dollar Bills, Bibliography
————. 10. Wheels,
Life and Other Mathematical Amusements (1983). W. H. Freeman and Company. Hardback
(18 August 2011)
1 Wheels, 2 Diophantine
Analysis and Fermat's Last Theorem, 3 The Knotted Molecule and Other Problems,
4 Alephs and Supertasks, 5 Nontransitive Dice and Other Probability Paradoxes,
5 Geometrical Fallacies, 6 The Combinatorics of Paper Folding, 7 A Set of
Quickies, 8 Ticktacktoe Games, 9 Plaiting Polyhedrons, 10 The Game of Halma, 11
Advertising Premiums, 12 Salmon on Austin's Dog, 13 Nim and Hackenbush, 14
Golomb's Graceful Graphs, 15 Charles Addams' Skier and Other Problems, 16 Chess
Tasks, 17 Slither, 3X+1, and Other Curious Questions 18 Mathematical Tricks
with Cards, 19 The Game of Life, Part I, 20 The Game of Life, Part II, 21 The
Game of Life, Part III
————. 11. Knotted Doughnuts and Other Mathematical
Entertainments 1986. W. H. Freeman and Company. (8 January
1 Coincidence, 2 The Binary Gray Code, 3 Polycubes, 4 Bacon's Cipher, 5
Doughnuts: Linked and Knotted, 6 The Tour of the Arrows and Other Problems, 7
Napier's Bones, 8 Napier's Abacus, 9 Sim, Chomp and Racetrack, 10 Elevators, 11
Crossing Numbers, 12 Point Sets on the Sphere, 13 Newcomb's Paradox, 14
Reflections on Newcomb's Paradox, 15 Reverse the Fish and Other Problems, 16
Look-See Proofs, 17 Worm Paths, 18 Waring's Problems, 19 Cram, Bynum and
Quadraphage, 20 The I Ching, 21 The Laffer Curve
————. 12 Time Travel and Other Mathematical
Bewilderments 1988 (11 October 2011)
1 Time Travel, 2 Hexes and Stars, 3 Tangrams, Part 1, 4 Tangrams, Part
2, 5 Nontransitive Paradoxes, 6 Combinatorial Card Problems, 7 Melody-Making
Machines, 8 Anamorphic Art, 9 The Rubber Rope and Other Problems, 10 Six
Sensational Discoveries, 11 The Császár Polyhedron, 12 Dodgem and Other Simple
Games, 1. 3 Tiling with Convex Polygons, 14
Tiling with Polyominoes, Polyiamonds, and Polyhexes, 15 Curious Maps, 16
The Sixth Symbol and Other Problems, 17 Magic Squares and Cubes, 18 Block
Packing, 19 Induction and Probability, 20 Catalan Numbers, 21 Fun with a Pocket
Calculator, 22 Tree-Plant Problems
Of note is that this highlighted
contient forlenget Cairo references p.176,
and includes a little extra to the text per se , with It underlies… p. 171 (the
original article in Scientifiquement américain
contained just three) and Gardner’s
enigmatic quote of street tiling and unsubstantiated claim of mosaics of
Moorish building. Dunn’s reference was included, from which he is likely taking
of interest is his Chapter 7 on speculations as to ‘melody making machines’, of
a mechanical procedure of producing music, that can in theory be applied to
tiling life-like tessellations.
————. 13. Penrose Tiles to Trapdoor Ciphers. W. H.
Freeman and Company 1989 First edition 1989 (10 November 2007)
1 Penrose Tiling, 2 Penrose Tiling II, 3
Mandelbrot's Fractals, 4 Conway's Surreal Numbers, 5 Back from the Klondike and
Other Problems, 6 The Oulipo, 7 The Oulipo II, 8 Wythoff's Nim, 9 Pool-Ball
Triangles and Other Problems, 10 Mathematical Induction and Colored Hats, 11
Negative Numbers, 12 Cutting Shapes into N Congruent Parts, 13 Trapdoor
Ciphers, 14 Trapdoor Ciphers II, 15 Hyperbolas, 16 The New Eleusis, 17 Ramsey
Theory, 18 From Burrs to Berrocal, 19 Sicherman Dice, the Kruskal Count and
Other Curiosities, 20 Raymond Smullyan's Logic Puzzles, 21 The Return of Dr.
Matrix, Name Index
————. 14. Fractal
Music, Hypercards and More…. W. H.
Freeman and Company 1992 (7 February 2013)
1 White, Brown and Fractal Music, 2 The Tinkly Temple Bells, 3
Mathematical Zoo, 4 Charles Sanders Peirce, 5 Twisted Prismatic Rings, 6 ils
Thirty Color Cubes, 7 Egyptian Fractions, 8 Minimal Sculpture, 9 Minimal
Sculpture II, 10 Tangent Circles, 11 The Rotating Table and Other Problems, 12
Does Time Ever Stop? Can the Past Be Altered? 13 Generalized Ticktacktoe, 14
Psychic Wonders and Probability, 15 Mathematical Chess Problems, 16 Douglas
Hofstader's Gödel, Escher, Bach, 17 Imaginary Numbers, 18 Pi and Poetry:
Some Accidental Patterns 19 More on Poetry, 20 Packing Squares, 21 Chaitin's
6 is on MacMahon and his cube
————. 15. ils
Last Recreations. Copernicus An imprint of Springer-Verlag 1997 (26 March
1 The Wonders of a Planiverse, 2 Bulgarian Solitaire and Other Seemingly
Endless Tasks, 3 Fun with Eggs, Part I, 4 Fun with Eggs, Part II, 5 The
Topology of Knots, 6 M-Pire Maps, 7 Directed Graphs and Cannibals, 8 Dinner
Guests, Schoolgirls, and Handcuffed Prisoners, 9 The Monster and Other Sporadic
Groups, 10 Taxicab Geometry, 11 The Power of the Pigeonhole, 12 Strong Laws of
Small Primes, 13 Checker Recreations, Part I, 14 Checker Recreations, Part II,
15 Modulo Arithmetic and Hummer's Wicked Witch, 16 Lavinia Seeks a Room and
Other Problems, 17 The Symmetry
Creations of Scott Kim, 18 Parabolas, 19 Non-Euclidean Geometry, 20 Voting
Mathematics, 21 A Toroidal Paradox and Other Problems, 22 Minimal Steiner
Trees, 23 Trivalent Graphs, Snarks, and Boojums
————. (editor.) Mathematical Puzzles of Sam Loyd. Dover
Publications, Inc., New York
1959. (30 April 1994). Selected (from Loyd’s 1914 work Cyclopaedia of Puzzles),
and edited by Martin Gardner, with his own introduction.
Typical Loyd fayre.
————. (editor) More Puzzles and Curious Problems.
Henry E. Dudeney. Fontana
Books 1970. First published in Great
Britain by Souvenir Press under the title
‘536 Puzzles and Curious Problems’. (19 July 1992)
————. (editor) Puzzles and Curious Problems. Henry E.
Dudeney Fontana Books 1970. (First published in Great Britain by Souvenir Press
under the title ‘536 Puzzles and Curious Problems’) (8 August 1993)
————. The Ambidextrous Universe. Left, Right, and
the Fall of Parity. Penguin Books 1970. (14 June 1995)
Many aspects of interest
(albeit largely outside of tessellation), too numerous to list. Especially see
Chapter 4, Magic, of a wordplay nature.
————. The Annotated Alice. Penguin Books
1970 revised edition. First published 1960
(5 June 2013)
————. Codes, Ciphers
and Secret Writing. Dover Publications Inc, New York. 1984, Unabridged and
unaltered republication of the work first published by Simon & Shuster,
Inc, New York, 1972 (23 August 1994)
Popular account. Of note is
Thomas Jefferson’s wheel cipher invention, p. 59.
————. Puzzles from Other Worlds. Fantastical
brainteasers from Isaac Asimov’s Science Fiction Magazine. Oxford University
Trykk. 1989 (24 October 1998)
Gardner, Martin. Gardner’s Whys & Wherefores. Oxford University
Press 1990 (5 October 1996).
speculations. Pentominoes pp. 92-93.
————. More Mathematical Puzzles of Sam Loyd. Dover
Publications, Inc., New York
1960. (30 April 1994)
————. Science Magic. Martin Gardner’s Tricks &
Puzzles. Sterling Publishing Co., Inc. 1997 (not dated, c. 5 years ago)
Hocus-Pocus. The Autobiography of Martin Gardner. With a foreword by Persi
Diaconis and afterword by James Randi. Princeton University Press, 2013 (16
Pleasant coffee time reading.
Gives a good story of the great man in the round. A few snippets that I was
unaware of: his association with Salvador Dali. No Escher, perhaps
surprisingly. Mathematically, of most interest is Chapter 15, pp. 134-149, with
his association with Scientifiquement américain.
I was less than enamoured with the practical joke supposed humour of his friend
Garfunkel, Solomon. For all Practical Purposes.
Introduction to Contemporary Mathematics. (COMAP) W. H. Freeman and Company
Third edition1994 (First edition 1988). (30 April 1994)
Various aspects of
mathematics, most outside of my interest (and understanding). Popular level, of
16-year-old. Probably best described as a compilation from other sources. Les propriétaires étaient
scattered throughout are various tiling matters and ‘spotlights’/biographies,
such as Angels and Devils. pp. 642-643. Stanford teapot p. 647. Reference to
par hexagon, pp. 701, 716. Of most interest are Chapter 21, on Symmetry and
patterns, and Chapter 22, Tilings pp. 693-722. Includes Escher-like tilings,
Marjorie Rice, Penrose tiles, Quasicrystals. Various colour plates with a
tiling theme, Penrose, Escher’s works, Hyperbolic tilings, Marjorie Rice.
Geary, A. and H. V. Lowry, H. A. Hayden. Mathematics for
Technical Students Part One. Longman, Green and Co. 1954. First published
1938 (21 June 1992)
Typical generic maths text
book of the day, one of many that I have; simply, one would have sufficed. I do
not believe that I have used this in any way; the material being mostly beyond
my understanding. Very much of its day, with calculation to the fore, with
chapters on arithmetic, algebra, geometry, mensuration and trigonometry.
Reference to the dissection of square to rectangle paradox of 64 and 65 units,
Gellart, W et al. The VNR Concise Encyclopedia of
Mathematics. Van Nostrand Reinhold Company 1977 First saw c. 1986 (27
Ironically, one of the first maths books I ‘studied’! c. 1986.
Gerston, Judith (Series Editor) The Human Body (series) The Eye Window to the World. Torstar Books
Inc. 1984 (2 August 2014).
Although obviously not
strictly a maths book (A part work on the human body, with here eye), included
here as Escher is featured p. 125 Other World, and pp. 140-141, Convex and
Concave and with an essay (author unknown) ‘M. C. Escher Impossible Worlds’,
albeit nothing of significance. Escher print is also featured in ‘Brain’ in the
series, not obtained.
Gettings, Fred. ils
Meaning and Magic of Art. Paul Hamlyn Ltd. 1963 (18 April 2015)
Although a book on art rather
than mathematics, included as it has many crossover references on mathematical
matters, such to the golden section, notably pp. 36-43, but of the usual
nonsensical type. Snowflakes, spirals and curves pp. 64-65. Also, analysis of
pictures by overlaying of lines without any foundation whatsoever. Ideally
requires rebutting, but I have no time for now.
Of note is that it can be seen
that Mottershead shamefully appropriates Gettings’ diagrams on (p. 128 of
Sources…’) without any mention of Gettings!
Ghyka, Matila. The Geometry of Art and Life. Dover
Publications, Inc. New York
1977. First published 1946 (30 April 1994)
A brief chapter on tiling,
Chapter 5, of which a mistake is made re demi regular tilings, as noticed by
Grünbaum. The book is somewhat curious, with many instances of picture analysis
based on the golden section. I remain to be convinced (as with other books,
such as Mario Livio, pp. 167-168) that the artist set out with this intention
(and of other ‘harmonic division’, e.g. plate LXX). Far too much wishful
thinking is involved, with lines chosen as to the artists’ interpretation as
regards ‘best fit’ (or none at all as far as I can see in plate LXX!). Of no
Gibbons, Stanley. Stanley
Gibbons Stamp Catalogue Part 4 Benelux. 5e edition, 2003. (7
Although this cannot in any
way be described as a maths book, and indeed a book itself, being of a
catalogue, I nonetheless include here. The reason for its inclusion is that two
of Escher’s stamps are shown, on pp. 309 and 371, of the Netherlands Antilles
and Suriname respectively. However, there is little else by means of detail,
albeit an exact date of issue is given i.e. day and month, which was previously
unknown, although in itself this is of no consequence. Note that Part 4
reference to a 22-volume set; and is not of a series of the Benelux as might
otherwise be imagined by the title.
Gibbons G. W., E. P. S. Shellard, S. J. Rankin. The Future of Theoretical Physics and
Cosmology: Celebrating Stephen Hawking (Google excerpt) (15 June 2015)
Gibson, Walter B. Magic
with Science. William Collins & Co. Ltd, 1970. (9 January 2016)
Although of a science premise
of a children’s book, is included here as it has a small chapter on recreational
mathematics: ‘Geometrix (sic) ‘Tricks Involving Geometrical Principles’, pp. 107-114.
Included are Mobius strips and lost line, and Hooper’s cut. (Hooper is
mentioned in the introduction).
Gill, George; publisher. (Author and date published oddly not
stated; c. 1900?). Gill’s New School
of Geometry. George Gill and Sons, Minerva House, Warwick Lane, E.C. (9 July 1994)
Subtitled practical plane and
solid geometry. Typical generic geometry text book of the day, one of many that
I have; simply, one would have sufficed. The reason for obtaining the book was
to be able to look up any geometric construction as and if required, but I do
not believe that I have used this in any way. Geometrical tracery, pp. 111-115. Minor tilings p. 111.
Gjerde, Eric. Origami
Tessellations. Awe-Inspiring Geometric Designs. A. K. Peters Ltd, 2009
Complimentary copy from A. K.
Peters for using my Pólya bird bird tessellation, as an ‘overview’, p. 2. (From
the Leeuwarden 2008 Bridges art exhibit)
Glendinning, Paul. Maths
in Minutes. 200 Key Concepts Explained in an Instant. Quercus, 2012 (20
Small-format book, of a
pleasing, coffee-time reading nature. However, most of the concepts are beyond
my understanding. Disarmingly, for someone of Glendinning’s stature, a professor
of applied mathematics, he is one of many with a fallacious belief of the
Golden Ratio appearing in the Parthenon, p. 37. His own example is particularly
excruciating. Further, the often seen Nautilus shell associated with the Golden
Ratio features on the cover, of which this is seemingly implied, although,
oddly, is not discussed in the book. Has a chapter on Geometry, pp.108-162,
with tessellations pp. 148-149, Penrose tilings pp.150-151.
Glenn, Robert. Foundation Maths. For GCSE and Standard
qualité. Heinemann Educational Books Ltd 1988 First saw c. December 1990, a
date of study (15 January 2001)
Textbook,12-year- old target
audience. Escher's swan outline used p. 49, unaccredited. Pattern, tessellation
pp. 115, 117, 197-198 barely worth mentioning.
Glenn, William H. and Donovan A. Johnson. The Theorem of
Pythagoras. Exploring Mathematics on Your Own. Volume 4. John Murray, First published in Great Britain 1964,
Reprinted in 1965 (24 October 1998 and 22 October 2005) Two books
Small format hardback, 48 pp.
Volume 4 of a 17-book series (none ostensibly on tessellation) of what is
clearly intended for juvenile audience, although not stated as such. Without a
doubt, readable, and ideally I would re-read, as for me at least it gives a incroyable introduction to the Pythagoras Theorem, with numerous illustrations,
although at times the mathematics is beyond me (and to an extent of interest
too). Obtained in conjunction with volume 3, at a sale.
————. Number Patterns Exploring Mathematics on Your Own 3.
John Murray 1964 (24 October 2005)
Gleick, James. Chaos. Making a New Science. Sphere Books
Ltd. 1990 (21 July 1996)
Goldberg, Kenneth P. Learning
Commodore 64 Logo Together. An Activity Book for Creative Parents, Teachers,
and Kids. Microsoft Press 1984. (21 February (1998?)
Early days of computing, and
so all rather dated. Nothing of any
interest now. Of most note (relatively) is a small subchapter on ‘Polygon
Patterns’, pp. 142-152, with simple geometrical drawings and occasional tilings
Goodstein, R. L. Fundamental Concepts of Modern
Mathematics. Pergamon Press 1964 (31 October 1996)
Of very limited interest. Chapter
5, Networks and maps (topology) pp. 241-268.
Golomb, Solomon W. Polyominoes. Puzzles, Patterns, Problems,
and Packings. Revised and expanded second edition. Princeton University
Press 1994 (2 February 1998). Original edition 1965
The bible of polyominoes; ikke
that I’ve done much with it!
Gombrich, E. H. The Story of Art. First Published 1950. 1972 Phaidon Press (9 October 2005) 498 pp.
Gombrich, a noted art historian, has written many landmark books, including some of direct interest as to mathematics and Escher, of which it is thus not always easy to recall specifics. Therefore, I include 'all' here, even though not all bear any relation to mathematics and Escher, as indeed this is an instance. I checked the contents and index for any possible direct interest, of which there is essentially nothing. Much time could be wasted upon a casual browse through so many pages, and so I thus refrain from further investigation.
and illusion: a study in the psychology of pictorial representation: the A.
W. Mellon lectures in the fine arts, 1956, National Gallery of Art, Washington by Gombrich, E. H. (Ernst Hans), 1909-
I can’t remember if I have
this; perhaps I am confusing it with other books by Gombrich.
————. Meditations on a
Hobby Horse and Other Essays on the Theory of Art. New York: Phaidon, 1963
Illusion and Visual Deadlock, pp.
151-158. Many Escher references and illustrations in the chapter. Originally
published under the title ‘How to Read a Painting’ in the Adventures of the Mind, series of the Saturday Evening Post, July 29, 1961. Note that Escher’s Horseman
tessellation is used for the cover of a subsequent later edition.
————. The Sense of
Order: A Study in the Psychology of Decorative Art. Second edition, Phaidon
Press Limited, Second Printing 1980 (Date unknown, c. 2005) First published
1979 (First saw 1988, Grimsby Art School library)
Has occasional tessellations
aspects, but this book continually flatters to deceive; it’s more of ornament
in the broader sense than tessellation. Many aspects of interest. Has Escher
boat and fish p. 89, Escher-like tessellation by an unknown Japanese, Michio
Kubo, dated 1968 on p. 91. Frequent occurrence is the term ‘counterchange’
applied to any black and white tilings. I much prefer my own usage! The book
has an excellent bibliography, with many books not commonly mentioned, most of
which are worthy of following up. Gombrich is seemingly the popularizes,
following up Stuart Durant (the circumstances of which is not detailed), of
Douat’s Truchet tiling follow-up, pp.70-72.
Goodfellow, Caroline. jeu
& Puzzles. The Collector’s Guide to Indoor Games from The 1700s to the
Present Day. Eagle Editions Ltd, First
edition 2002 (24 November 2018)
A most pleasing scholarly
approach, of a popular level. 128 pages. Of most interest is Chapter 7 ‘The
Early Jigsaw’, pp. 110-117. Other chapters remain of interest, indirectly.
Previously, I was unaware of
Goodfellow. I see that she has written a variety of bygone games, dolls, toys type
books, and of which I see that she was previously curator of dolls and toys at
ils Victoria and Albert Museum, and a member of Board Game Studies, an
international society of experts on board games, a body of which, again, I was
unfamiliar! Likely now that I am familiar with her name I will chance upon it
upon game book reading.
Gorini, Catherine A. ils
Facts on File Geometry Handbook. 2003, 2009 revised edition. Facts on File
Inc, and imprint of Infobase publishing
Cairo tiling illustrated p. 22, equilateral. Gives the
following definition: Cairo tessellation: A tessellation of the plane by congruent convex equilateral pentagons
that have two nonadjacent right angles; so called because it can be found on
streets in Cairo.
Graham, Christine. Mathematics GCSE.
1987 Revision book.
Tessellation barely mentioned;
just one line.
Green, Patrick. Seeing is Believing. Vineyard Books
1996 (27 January 2007)
Juvenile. Escher’s House of
Stairs p. 34. The Escher reference, a single picture with no text is so
unimportant to be barely worth mentioning. Indeed, ‘Escher’ per se does not get
a mention; the book shows just his print!
Gregory, Richard L. ils
intelligent eye. Weidenfeld & Nicolson, 1970 (18 August 2015)
Minor use of Escher's
pictures, Waterfall and Belvedere, pp. 52-53 to illustrate paradoxes of depth, with
a brief commentary, of no particular insight. Of note is that this book was
first seen in 1987, likely in college library.
Gregory, Richard L & E. H.
Gombrich (eds.). Illusion in Nature and
art. Duckworth, First published 1973 (4 May 2017) First saw 1987
reference in Visions. Of general
interest. Six scholarly psychology-led chapters, with contributions from Colin
Blakemore, R. L. Gregory, H. E. Hinton, Jan B. Deregowski, E. H. Gombrich and
Roland Penrose. The essays are a little obscure, of which time spent studying
‘in depth’ would be disproportionate as to worth.
Purposefully latterly obtained (2017) as part on my
ongoing 1987 review, as this was studied in 1987, the essence of the book being
long forgotten. Minor, inconsequential Escher references, as regards impossible
objects rather then tessellations, of just a few lines (no illustrations) pp.
86, 280. Skim read.
The book has as its origin the setting up an exhibition
initiated by Sir Roland Penrose, at the Institute of Contemporary Arts, London.
Of note is p. 207 and Bust of Voltaire by Houdon, and the ‘projecting eye’
Gregory, Richard L. Eye
Small format paperback.
Gribbin, John and Mary Gribbin. Big Numbers. Wizard Books, 2003 (no date)
On numbers in science, rather
than a mathematics book per se. Popular account. Occasional browse. P. 68
explains why toadstools have long stalks, the reasons of which I didn’t know
Grünbaum, B. and G. C. Shephard. Tilings and Patterns.
W. H. Freeman and Company New York, 1987 (11 January 1993; first saw in 1989)
The bible of tiling and mind
boggling in its depth! Indispensable, although much is way too advanced for me.
Largely, indeed overwhelmingly, academic, but still accessible on occasion. Cairo-esque
s. 480, as part of the 24 polygonal isohedral types of proper tilings by
pentagons. And much more beside!
Greer, A. A Complete GCSE Mathematics Higher Course. Stanley Thornes
(Publishers) Ltd. 1989 (15 October 1995).
Textbook. Tessellation pp.
297-300, very basic, barely worth mentioning.
Guinness Word Records. Guinness World Records Limited. 2002. (17 December 2016)
Although not a maths book per se, obtained as
Götz-Peter Reichelt’s cluster puzzle Noah’s Ark is mentioned (and illustrated),
although oddly no reference is made to the interlocking premise.
Jan. Mathematics From the Birth of
Numbers. W. W. Norton & Company, New York London (7 August 2016, first
saw in Grimsby library, at least 2001)
A weighty tome, of 1093 pages! Minor reference to
tessellation, p. 395 (albeit with poor quality diagrams) and Escher, p. 375.
S. Vermischte Untersuchungen zur
Geshichte der Mathematischen Wisssenschaft. Leipzig, 1876. (Downloaded from
GDZ site 29 April 2015)
From a reference in Bradley. Somewhat of a let-down;
no tiling. Mostly of an academic nature, text heavy, with occasional geometric
diagrams throughout the first part of book, and polyhedra pp. 36-37, with
Kepler references. Of no practical use.
Guy, Richard K. and Robert W. Woodrow (Editors). The Lighter Side of Mathematics.
Proceedings of the Eugène Strens Memorial Conference on Recreational
MAA Spectrum, 1994. (18 January 2012)
In three main parts: 1 Tiling
and Colouring, 2 Games and Puzzles, 3 People and Pursuits. Many aspects
referring to tiling and Escher in Part 1. Of special note:
Escher: A Mathematician In
Spite of Himself, Doris Schattschneider (first appeared in Structural Topology, 1988)
Fun with tessellations, John
Escheresch, Athelstan Spilhaus
Henry Ernest Dudeney:
Britain’s Greatest Puzzlist, Angela Newing (has much detail on Dudeney not
The Utility of Recreational
Mathematics, David Singmaster
Puzzles Old & New: Some
Has Escher bird tiling on
front cover Locher 361A, April 1949
Hall. Dorothea (ed). Memories
of Childhood. Chartwell Books Inc 1990 (26 June 2016)
Hambidge, Jay. The Elements of Dynamic Symmetry.
Dover Publications, Inc. New York
first published by Dover
1967, a reprint of 1926 edition (30 April 1994)
I don’t quite know what to
make of this book. It gives a lot of ‘dynamic symmetrical’ constructions
involving squares and rectangles, but I largely remain to be convinced of its
efficacy. I recall someone somewhere describe Hambidge as a crank. Indeed,
Mario Livio for one is of this opinion, see p. 171 in which he largely
discredits his work, or at least implies this. Whatever, the book is of limited
appeal. No tessellation.
Hanby, G. A. Geometry I . (First saw 19-20 March
Hand, William. ‘Scientific Mysticism’ in Rosicrucian Heritage Non. 1 2005. (9 June
Use of Escher's print Print Gallery, p. 21; no other mention
of Escher in article.
Hannas, Linda (Introduction). To
Hundred Years of Jigsaw Puzzles. Exhibition catalogue of 1968 at the London
Museum, 40 pages, with introduction by Linda Hannas (19 November 2016)
Jigsaw Puzzle interest. Slim booklet of 40 pages, skrevet
for the London exhibition of 1968, with much input by Hannas. A speculative purchase, være en
commonly-quoted book in jigsaw puzzle circles in the hope of detail of direct cluster puzzle interest, of
which there is indeed one of note, namely an entry for Mrs Elspeth Eagle-Clarke,
s. 37, albeit without a picture. However, disarmingly, two mistakes are made in
the text, with ‘Miss’ rather than Mrs and ‘Clark’ rather than Clarke. En annen
mistake is on p. 10, where the previous eagle-eyed buyer had noticed an
incorrect date on a John Wallis publication and duly corrected, not 1768 but
rather 1788. Of note is the caption:
66. Dragon’s Land 1934 Manufactured
by Chad Valley Co Ltd.
17 x 15½ in. Colour print
of design by Miss (sic) Elspeth Eagle-Clark (sic). Each piece is a picture in
itself dovetailing into a complete design London Museum 67.92/2.
An original picture of 1930 mounted on plywood in 1967 by the
same craftsman at the Chad Valley Works who cut the prototype in 1934’.
The last sentence is full of ambiguity as to meaning. I tried to
resolve this with Anne Williams, but to no avail.
Eagle-Clarke aspects aside,
the book is full of historical aspects of interest.
————. The English
Jigsaw Puzzle 1760-1890. Wayland Publishers, London, 1972 (22 October 2014)
Jigsaw puzzle interest. Obtained
primarily in relation to possible interest regarding cluster puzzles, this
being a commonly-quoted book in jigsaw puzzle circles. As such, for min specific purposes, somewhat of a let
down; there is nothing cluster puzzle-related, not that I was really expected
anything in this field. But one never knows…. As such, it consists mostly of
text, with relatively few pictures. I think it would have been improved by
more. However, as regards its true purpose, of a historical account, then it is
indeed ideal, and indeed a pioneering work of outstanding scholarship. Indeed,
Hannas must be lauded for her quite outstanding research. That of John
Spilsbury is quite outstanding.
an aside, perhaps of most note is an illusion, plate 14, titled ‘Before and
after Marriage’ of 1789, of two heads that when turned upside down resemble another
picture. This needs investigating the historical aspect; I cannot recall having
seen this before.
shows a later version of this, of 1884.
————. The Jigsaw Book.
Celebrating two centuries of
jigsaw-puzzling round the world. Bellew & Higton Publishers, 1981. (16 January
Jigsaw puzzle interest. Même si
not of a mathematical nature, included as regards my investigations into
cluster puzzles, and the author being of note per se in the jigsaw community. Likely
a purposefully, more popular account than her more serious books. Relatively
lightweight, of just 91 pages. Nothing at all in the way of cluster puzzles.
However, of sight interest is p. 91, where a puzzle has been cut into a
tessellation premise of a broad single tile. Also of indirect interest is a
generic Hamley brother puzzle ‘Society Dissected Picture Puzzle’ label, p. 18,
although this does not appear to have been captioned or discussed. Also has
‘Before and after Marriage’ of 1789, p.11.
Harbin, Robert. Origami
1. The Art of Paper-Folding.
Coronet Books, 1974. First printed 1968 by Teach Yourself Books as Teach Yourself Origami (15 August 1993)
The first of a three-book
series, all of a like nature, with a brief introductory discussion of a few
pages, followed by diagrammatic instructions. Only of minor interest, in
passing, and not studied as such. As such, there is nothing here overtly
mathematical, but I include here nonetheless, as paper folding can loosely be
regarded as ‘mathematical’ in nature.
————. Origami 2. The Art of Paper-Folding. Previously
published as More Origami. Coronet
Books, Eleventh impression 1975 (26 June 1994)
As detailed above.
————. Origami 3. The Art of Paper-Folding. Coronet Books,
Fourth impression 1975 (26 June 1994)
As detailed above.
Hargittai, István; Hargittai, Magdolna. Symmetry A
Unifying Concept. Shelter Publications Inc. 1994 (10 August 2006)
Popular account of symmetry,
very pleasing. Escher pp. 191-192, 207. Fish and Boats, E113; Bird and Fish
E115; Bat, Bird, Bee, Butterfly 81; Bulldogs E97; Pegasus E105. ‘Japanese Cairo’
tiling p. 174.
Harris, Ella & Caroline Christin (eds). Puzzle Chest. Barnes & Noble Books,
Sterling 2003. (5 July 2015)
A compilation of a series of
Sterling books on a puzzle theme, of a juvenile audience. See p. 177 for
‘Jockeys on Ponies’, of a Loyd premise, p. 221 for possible Sam Loyd source of
two donkeys, and p. 229 for a discussion of Schuster’s ‘three-stick clevis’.
The book largely flatters to deceive. For instance, the Penrose tribar is used
in many different trivial forms throughout. A typical illusion book in that
well-known illusions are repeated without any fresh insight, or indeed novelty.
Hatton, Richard G. Design.
An Exposition of the Principles and Practice of the Making of Patterns.
London Chapman and Hall Ld, 1902 (Internet book archive, 20 October 2015)
Downloaded upon a general
search on the off chance that it may possibly contain tiling in some form. As such,
not really; although it has loose elements, but nothing is entirely
satisfactory. Probably the best chapter is pp. 149-165, of Lewis Day-esque, but
I am not planning on revisiting this.
Hayman, Margaret. Essential Mathematics: A Modern
Approach to CSE. Macmillan Education. 1979. (13 December 2000)
Heesch, H. and O. Kienzle. Flächenschluss. System der
Formen lückenlos aneinanderschliessender Flachteile. Springer-Verlag, Berlin
1963 (in German) (2010) PDF
In German, 135 pages, somewhat
hindered by a lack of translation. Seems so many diagrams of interest, but understanding
them in a foreign language is the difficulty. Tilings pp. 1-3, 34-36, 52,
64-77, 80, 85-89, 98-107, 114-115, 120-129. No ‘true’ Cairo or pentagon studies, at least as far as
I can make out. Quoted by Schattsneider. Schattsneider, p. 326, focuses on p? où
Heesch shows his Set of 28, including the Wikipedia paving, no. 9, although not
exact….. P. 68 shows the tile in detail.
Heesch, Heinrich. Reguläres Parkettierungsproblem (Regular tiling problem)1968 WANTED
————. Gesammelte Abhandlungen 1986. Translated: Heesch, Heinrich: Collected essays WANTED
Hemmings, Ray and Dick Tahta. Images of Infinity.
Tarquin Publications 1992 (First pubished 1984, of Leapfrogs Group) (3 June 1993)
Popular account of infinity, kanskje of a school-age audience, 96 pages. Oddly, the book does not have a contents
or introduction, or indeed, any structure at all! Escher’s Circle Limit I, p. 14, albeit without explanation or caption! Pentagons
p.57, Dart tessellation (in context of quadrilaterals) p. 72. Escher inspired ‘hand
drawing hand’ pp. 3, 46. Liberally illustrated, in black and white pen
drawing, and early computer drawings, now somewhat dated. As such, the book is
lacking, for reasons as outlined above. A pleasant enough read, but there is
nothing of any real substance here.
Infinite Design Allover Patterns.
Dover Publications, Inc. New York.
1985 (15 October 1995)
Various tessellations, of 46
plates, in outline form. Of no consequence, being unstructured. Would appear to
be intended as a child’s colouring-in book. Trivial.
Hendricks, Gordon. Eadweard
Muybridge: The Father of the Motion Picture, Grossman Publishers, 1975
(First saw, or at least recorded, 9 August 1988, Grimsby central library)
A minor study, of 9 and 23
August 1988, of an indirect manner of Escher-like tessellation, in which I
studied various animal’s outlines, as with this book, featuring horses, of a
five-sheet study. However, this type of study is no longer active, and of which
my interest essentially peaked and ended in 1988. The study, such as it was,
consisting of photocopying horse motion photographs of interest and then
assembling for easier viewing.
The book is largely long forgotten and although this is available on the internet archive,
and at bookstores of an accessible price, as this particular study is no longer
active I shall not pursue this.
Heritage, R. Learning
Maths Book 1 (first saw 14
Has minor tessellation, with a
novel design method, not fully understood, and two Escher-like tessellations of
a cat’s head with gaps and a fish? showing no understanding of the issues. Much
to my annoyance, I cannot now find details of this book online, at Bookfinder,
or elsewhere. Likely this was a primary or secondary school oriented.
Hessemer, Friedrich Maximilian. Arabische und Alt-Italianische Bau-Verzierungen. Berlin, G. Reimer, 1842. Translated: 'Arabic and Old Italian Construction Embellishments'. (2013).
Has many plates of decided interest. Especially see fused pentagon. First drawn to my attention by Pail Tucker, 2013. Available on Internet Archive.
Heyden Van der, A. ils
Glory of Egypt. Wunderbares Ägyten / Les Splendeurs d'Egypte Amsterdam,
Elsevier u. Kairo, Al Ahram, 4th printing, 1982. (19 September 2015)
English, German, French book,
on ‘sights’ of old Egypt, rather than of modern-day street scenes. Cairo tiling
at the Old Cataract hotel seen from afar, diagram 39 (book is unpaginated!),
although the sighting is strictly not merkbar, with foreknowledge required,
albeit this can only indeed be the paving. This is now the earliest recorded
sighting at the Old Cataract Hotel, and likely of 1974, in a earlier edition,
but not seen.
Hicks, G. A. Moderne
Technical Drawing Vol. 2 1971 (from a c. 1987 study)
A minor geometrical
construction study of no consequence. This was a library book and is not in my
possession. I do not recall the book in any way.
Higgins, Muriel. New
Designs from Machine Patchwork. Charles Scribner’s Sons, New York, 1980 (23
Chance finding. Has much of
tessellation interest than others of its type, hence its purchase. Of particular
note is an tiling based upon the well known eight pointed star and pointed
cross inspired by Islamic geometry, p. 123 with an additional tile. Although of
a most simple nature indeed, I do not recall having seen this previously. sur
research, I see that the eight pointed star and pointed cross is known as the
‘Breath of the Compassionate’, a seemingly new term to me. However, upon yet
more research, I see that it is mentioned in Chorbaci’s paper, but had been
forgotten! Also see Abbas, where this is named ‘Khatem Sulemanii’.
Ester Harris. The How and Why Wonder Book
of Mathematics. Transworld publishers London
1961 (21 June 1997)
Juvenile, with a leaning
towards historic aspects. Minor recreational aspects: Three utilities problem,
map colouring theorem, no tiling.
D. and S. Cohn-Vossen. Geometry and the
Imagination. Chelsea Publishing Company, New York. 1952.
An English translation of the German edition. A bitter disappointment,
in that it is far too complex for me (as I suspected), given the main author,
but I saw it recommended somewhere as being ‘recreational’!
Francis S. Jr. Computer Graphics.
Macmillan Publishing Company New York,
1990. (16 June 2011)
Hopelessly outdated, only obtained due to a known Cairo tiling reference, p. 145. Escher
tilings: p. 143 Horseman, Birds and fish p. 143, with a small tessellation
Article. Chapter 2 heading has a line drawing of Escher ‘Drawing Hands’ Chapter
5, p. 141, is concerned with tiling, despite a perhaps less than accurate title
‘Approaches to Infinity’; no other chapter heading has Escher's use. High and
Low p. 403, Ascending and Descending p. 408.
See p. 256 for famous graphics teapot (although there is no apparent
reference, save for bibliography, with F. C. Crow) Snowflake p. 171. Dudeney
dissection p. 382, although not credited.
Hillman, David. Pentagames. A colourful collection of
classic games designed by Pentagram. Guild Publishing 1990 (not dated, c
Largely a ‘coffee table’ book.
Puzzles, nothing per se specifically of pentagon theme as indicated by the title.
‘Pentagames’ is a brand name for a company
Hiner, Mark. Up-Pops.
Paper Engineering With Elastic Bands. Tarquin Publications 1996 (21 August
————. Phantasmagrams. A collection of visual and optical
illusions designed by Pentagram Ebury Press 1992 (not dated, c 10+ years).
Hoffa, Alan; Koss, Roberta. Focus on Geometry. Addison Wesley Secondary Math. 1998 (15 October
Tessellations pp. 242, 247,
253, 404-415. All inconsequential. 16-year-age.
Hoffman, Paul. The Man Who Loved Only Numbers. The story
of Paul Erdos and the search for mathematical truth. Fourth Estate, London 1999. First
published in 1998 (23 September 2006)
Accessible account of Erdos’
Hofstadter, Douglas R. Gödel,
Escher, Bach: An Eternal Golden Braid. Metaphorical fugue on minds and
machines in the spirit of Lewis Carroll. Penguin Books 1979 (First saw 21
December 1988 (recorded on a menu card), finally obtained 3 December 2006)
Many uses of Escher’s prints,
too numerous to mention here. Book is a bit quirky, if not downright odd.
Indeed, in a general sense, all of Hofstadter’s writings are quirky, to me at
least, but likely it’s just Hofstadter’s advanced nature that’s way beyond me! qui
such, I do not believe, that, unlike other Escher references, this was studied
in any way.
Themas: Questing for the Essence of Mind and Pattern. Basic Books; New
edition) 1996 First Printing edition 1985) (21 November 2016) PDF
Upon researching for parquet
deformation, as I do at random, in 2016 I stumbled across the work of David
Oleson, in which by circuitous means I found was featured in Hofstadter’s book.
This was a total surprise; I was under the impression that this was a simple
facsimile replication of his columns in Scientific
American, and of which as I had the more important ones and so did not
bother to pursue. However, this is not so, as evidenced by the Oleson finding!
How infuriating! And much time lost too. This is now re-titled ‘Parquet
Deformations: A Subtle, Intricate Art Form’ July, 1983 pp. 190-199.
————. Fluid Concepts and Creative Concepts. Computer
Models of the Fundamental Mechanisms of Thought. Allen Lane The Penguin Press 1997. (N. B.
The date has faded, 10 April 1999?).
A heavyweight tome, of 500+
pages, of largely of an academic nature, although readable, but obscure, with
numerous essays, albeit invariably of limited interest. A single page discussion
on Parquet Deformations, albeit without diagrams, p. 477. Scott Kim p. 403.
Nothing on Escher.
Hogben, Lancelot. Mathematics for the Million. First
Published 1936 George Allen. * 1940
and Pan Books Limited, 1967 paperback (7 March 1993
hardback; 16 April 1995 paperback)
Small format paperback, of 649
pages! From the title, seemingly of a popular level, although still notably
advanced for a generell readership. Liberally illustrated. Lots of equations.
The approach is indeed thorough, but largely beyond my interests and
understanding. There may indeed be some aspects of interest, but finding these
in such a lengthy book is not easy. Nothing really recreational, despite the
title. No tessellation, polyhedra, Escher. Pressures of time forbids a re-read.
The 1967 edition is described
as ‘extensively revised with additional material and tout à fait re-illustrated’.
————. Man Must Measure. The Wonderful World of
Mathematics. Rathbone Books, London
1955 (4 August 1996)
Holden, Alan. Shapes, Space, and Symmetry. New York
Dover Publications 1991 (earlier edition 1971). (19 November 1994, York)
Delightful, a popular account,
readily accessible, from the basics on onwards.
Holderness, Jean. GCSE Maths Foundation Level.
Causeway Books 1987 (4 November 1995).
Textbook. Tessellation pp.
315-316, simple, barely worth mentioning.
Holiday, Ensor. Altair Creative Colouring Books. Book 3.
(9 March 1996 (year semi legible))
Juvenile colouring book on
tilings, of insignificant worth detailing here. A major drawback is that it
lacks an index, making finding references awkward.
Dictionary of Mathematics. Longman 1980 (not date stamped, c.10+ years)
Tessellation p. 151,
Holme, Audun. Geometry
Our Cultural Heritage. Second edition, 2010, Springer (4 February 2017)
Academic in tone, of a chance
finding at a bargain price, and so bought. Oddly for a Springer book, riddled with
typos and minor errors in English, likely due to the translation from the
author’s native Norwegian to English. Overwhelmingly too advanced for me, albeit
with occasional recreational aspects, along with readable histories that may be
referred to as and when required. Minor referral to tessellations, of
Archimedean pp. 233-239, and symmetry of plane ornaments p. 445.
Holt, Michael and Ronald Ridout. Illustrated by Peter
Edwards. The Big Book of Puzzles.
Puffin Books 1976 (12 September 1993).
Small format paperback, 142
pp. Usual introductory puzzle fare of
all types, stated as ‘something for all the family’. The title is misleading;
it’s a standard size paperback! Stated as a compilation of puzzles old and new,
although of a scan I do not see anything new here. 153 puzzles with answers,
but is not listed as such as contents, which is not given. Has Escher-inspired
Relativity and Penrose staircase front and cover. No tessellation. Kort oppsummert,
just a ‘fun book’ on puzzles, and there’s nothing wrong with that, and not
intended to be for scholarly reference. One of many of its type.
Holt, Michael. What is
the New Maths? First published in 1967 by Anthony Blond Ltd. First saw and
studied 18 Sep 1986 (23 September 2000)
A small format hardback, of
just 99 pp. New maths subjects, with sets etc, in a recreational style aimed at
the parent with a child. Various aspects of recreational maths of mild
interest, but nothing more. No tessellation.
————. Mathematics in
art. Studio Vista: London, New
York: Van Nostrand Reinhold Company, 1971 (25 August 2016).
a reference in Schattschneider and Locher. A small format paperback, of just 96
pp, of six chapters, of a popular level. Escher frontispiece, pp. 42, 46,
49-50, 77-78, 83. Most of the Escher references are in passing only, and in
when ‘in detail’ are brief. Illustrated with Ascending and Descending, p. 46, and Horseman Mobius band, p. 77. Aside from Escher, has topics of
general interest, such as Penrose tribar, but nothing too important. as an
aside, this is typical of many of the books in Schattsneider’s listing of ‘Escher
appearances in books’, namely they are all relatively minor,
mentioned/illustrated almost in passing.
Hooper, Alfred. Makers of Mathematics. Faber and Faber
Limited. (24 August 1996)
Historical account. Newton, Leibniz, Gauss.
Some mathematics beyond me.
Hooper, W. Rational
recreations in which the principles
and numbers of natural philosophy are clearly copiously elucidated by a series
of easy entertaining interesting experiments. Vol II The second edition,
corrected. London 1774. (downloaded from Internet, 8 May
From a reference in MacMahon. aucun
mention is made of different volumes; the one I have, Vol. II, is purely on
general science, with a leaning towards optics; certainly, there is no
mathematics here at all.
Hopkins, C. H. Project Mathematics Stage four (sic)
Longmans 1967 (17 August 1997)
Hornung, Clarence P. Handbook of Designs and Devices.
1836 basic designs and their variations. Dover Publications, Inc. New York 1959 (28 March
1998). Note that this is a revision of a 1932 work
As such, no tessellating
designs at all; but that said, still of interests due to the geometric aspects.
The book leans towards the designs themselves, and although they are indeed discussed,
this is very much of a secondary aspect.
Hovanec, Helene. The Puzzler’s Paradise. Paddington
Press New York
1978 (16 March 1996)
Huberich, Paul G. ils
Master System of Short Method Arithmetic and Mechanical Calculations Simplified.
Max Stein & Company, 1951. First published by Joe Bond, 1924
Small format (square)
paperback, American, 128 pp. The cover states ‘Methods used by the world’s fremst experts. Adapted for home study’. Gives guidance on arithmetic, some of which I
have concerns with. s. 3 Arabic number beginning. Some seem desidert obscure,
beyond reason. e.g p. 21, to multiply any number by 16 2/3.
The merits of the procedures given I leave to others. Date stamping has
faded to point of illegibility. c. 1998? Also has other mathematical aspects,
perhaps peripheral to the title. en
short, of no practical benefit..
Huff, Darrell. How to Lie with Statistics. Penguin
Books 1988. (11 July 1998)
Popular small format paperback
account of statistics. However, of limited interest in the extreme, as I am not really
interested in the subject. Lacks an index, which would help to find terms as given on
the back cover. The seemingly basic ‘samples’ and ‘errors’ subcategories were
unfamiliar to me.
Irving, Washington. Treasures of the Alhambra. Geocolor, 1979 (6 August 1994, Lincoln)
Although not strictly a maths
book per se, included for its tiling aspect.
Isenberg, Cyril. Soap Film
Experiments. Manufacturers brochure, not dated. (13 July 1995)
Jacobs, Harold R. Mathematics A Human Endeavour. W. H. Freeman
and Company 1970 (18 June 2015)
semi-text book. The book is described as ‘a textbook for those who think they
don’t like the subject’, with a foreword by Martin Gardner, more or less aimed
at a sixteen-year-old school age. I’m not entirely sure quite what to make of
this; as such, it is in-between a recreational and textbook. Ten chapters, with
of note Chapter 3, Mathematical Mosaics, pp. 202-208 and Chapter 4, The Regular
Polyhedra, pp. 209-244. Certainly, there is nothing ‘new’ here for me. Uses
three of Escher's artworks: Horsemen, on cover, Waterfall p. 19, Horseman again
s. 207 and Möbius Band p. 478.
————. Geometry. W. H. Freeman and Company 1974 (25 August 2007) First saw
in Grimsby reference library c. 30 Jul 1987
Semi-popular, semi-text book
with 16 chapters, with each chapter subdivided into a series of lessons.
instances of Escher use throughout the book (although oddly not indexed), on
the cover, Ascending and Descending, Man
with Cuboid pp. 128, 227, Periodic Drawing 25 (Reptiles), 148 (and 153), Periodic
drawings of Beetles, Birds, Flatfish, Bulldogs all 227, 300 Birds and Fish,
Other World, p. 315, Circle Limit III
(of Angels and Devils) 469, Circle Limit III
s. 662. Oddly, aside from the first page, Escher is not mentioned elsewhere in
any of the other credits (and of which makes for finding references most
of interesting bits of geometry, at a largely accessible level. The book was first
studied in 30-31 July 1987, albeit somewhat chaotically, of which the study has
dated badly, and can be considered as next to worthless.
Oswald with William H. Benson. Mathematics
For Pleasure. Victor Golanz Ltd 1962 Not dated, c. 2000
Compilation of popular puzzles in the style of
Dudeney. Usage is made of Hubert Phillips (Caliban) work. Next to nothing of a
John. Rational amusements for winter
kvelder. London 1821 (downloaded from Internet, 11 May 2015)
From a reference in MacMahon, 200 pages. No tiling
or polyhedra, despite a promising lead with ‘geometric puzzle’ chapter, pp.
22-32 (31-40). Has geometric dissections. Overall the puzzles are relatively
simple, with the sub title refers to ‘young people’ in mind.
(ed.). Mathematics. An Illustrated
History of Numbers. Shelter Harbour Press, 2012 (16 December 2017)
A popular accent, liberally illustrated under four main groupings:
prehistory to the middle ages; the renaissance and the age of enlightenment;
new number, new theories and modern mathematics. A most pleasing read. Les propriétaires étaient
perhaps surprisingly, nothing on tessellation or Escher!
Jackson, Valerie (ed.). The Complete Book on Patchwork and Quilting. WI Books limited 1985
(11 June 2013)
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed, it is one of the better books there is
on the interrelation between the two, and indeed led to extensive studies of
the day (1987, as indeed with other patchwork books). However, now, and for
some considerable time, the nature of the material is considered hardly worthy
the time originally devoted to it.
James, E. J. Moderne
School Mathematics Books 1-4. Oxford University Press, 1959 (First seen
September 1987) A date of 16 September 1987 is recorded on a menu card
Seemingly part of a four-book
series, albeit of which the one I saw was
not recorded. From a reference on a shared sheet in Cundy and Rollett. The book
is long forgotten, I cannot picture it in any way, although the title seems
vaguely familiar. However, this above is not necessarily of the book, as James
has at least three other book to his name, but the title does indeed seem the
————. Curve Stitching. Oxford
University Press, 1962. From the series Mathematical Topics for Secondary
Schools. (Quoted in Murray-Rust) WANTED
Jamnitzer, Wentzal. Perspectiva
Corporum Regularium. Nuremberg
1568. (Downloaded from internet 10 June 2015)
On polyhedra. Has five main
sections, based on the platonic solids. Has many plates not commonly shown in
Jankel, Annabel and Rocky Morton. Creative Computer Graphics. Book Club Associates with Cambridge University Press, First published 1984
(13 June 2004). Oversize
Good popular account of the
early days of computer graphics. Of its time, and still of interest, albeit it has dated amazingly
Snippets of direct interest
include: p. 95, on Robert Abel, with an Escher-like image that from memory I
saw in the Appendix in Art and Science; without it I doubt very much I would
have noticed the association. This is from ‘Changing Pictures, TRW’, of which upon an initial look (2018) I could
not find freely available. Islamic computer generated tiling as background p.
16. Posted on Broug Ateliers as to the tidligste mulig forekomst (although
unlikely), with skuff results (two insignificant comments!)
Jaworski, John & Ian Stewart. Nut-crackers. Puzzles
and games to boggle the mind. Pan Books Ltd 1976 (14 October 2000)
Small format paperback, 125
pp. Typical children’s ‘fun’ paperback,
with 100 popular puzzles (with answers), albeit nothing more than a
compendium of well-known puzzles really. Lacks an introduction and index.
Escher-style illusions (no tessellations) are prominent, and indeed the cover
is a stylized version of Waterfall, et the back cover shows a Penrose staircase. Pp. 48-49 also refers to Waterfall.
the authors, Stewart is too well known to document, although Jaworksi is
decidedly less so. Upon research, he appears
to have been Stewart’s colleague at Warwick University, and editor of
Universitetet Manifold magazine. He
also wrote a piece on the Alhambra.
Jeger, Max (edited by David Wheeler). Transformation
Geometry. George Allen and Unwin Ltd. 1970. First published in England
1966. (Date not stated, as a guess, 2000)
Small format paperback, 143
pp. Part 1 of a five-book series. Translated from the German, with an English version by A.W. Diecke
and A. G. Howson. Advanced in nature, way beyond my understanding. Reference is
made to Escher and Terpstra in the bibliography. Oddly, there is no reference
to Escher in the text (I checked each page, 2018). Tessellation of sorts pp.
42-43, but in the context of vectors. Of limited interest and use in the
extreme. I have no plans to re-read.
Jenkins, Gerald and Wild, Anne. Mathematical Curiosities,
Books 1, 2 and 3. Tarquin Publications 1980, 1989 and 1990.
————. Make Shapes. Books 1, 2 and 3. Tarquin
Publications. 1990, 1990 and ?
Jenkins, Gerald and Magdalen Bear. The Final Stellation of the Icosahedron. Tarquin Polyhedra No. 3. Tarquin
Publications, 1985. (1 April 1993).
Nets to be assembled;
disappointingly, no text is giving at all concerning the background to this.
————. Paper Polyhedra
– in colour. A collection of 15 symmetrical mathematical models to cut out
and glue together. (25 October 2014). 2004, first edition 1998. Tarquin
A varied collection of polyhedra, to be assembled.
Jobbings, Andrew. Note 89.93. ‘Dissecting a triangle into
rectangles’. Mathematical Gazette
Vol. 89, 516 (November 2005) 501-502 (21 March 2013)
Johnson, Donovan A and William H. Glenn. The World of Measurement.
John Murray. 1964 (24 October 1998). Volume 2 of the 12 book series ‘Exploring
Mathematics on You Own’.
One of a series of five books
I have of a 12-book series, pitched at a juvenile audience, 12-year-old. cette
is mostly of ‘simple’ measurement calculation, of little interest.
————. Invitation to Mathematics. Exploring Mathematics on
Your Own. John Murray. 1964 (24 October 1998)
————. Understanding Numeration Systems John Murray. 1964
(24 October 1998)
Jones, Charles Booth-. More Brain Ticklers. Beaver Books
1978 (12 September 1993).
Jones, Christine. Roman
Mosaics. 1988. Not dated, c. 10 years+
This looks like a museum
booklet, of just 12 small pages, rather than a book per se.
Jones, Tim Glynne-. ils
Book of Numbers. Arcturus 2007 (24 January 2015)
Various commentaries on
numbers per se, albeit with many instances of numerology, and on occasion
incorrect mathematics, such as with the Golden Section.
Jones, Mike and Bibby, John. Recreational Mathematics
Resource Guide No. 5. (Year Unstated)
Jones, Lynn. Statistics. Macdonald Educational Colour Units 1974 (28 September 1997)
Note that this is not a book
in its own right, but part on a series on mathematics by the Macdonald
Educational, with other titles: Sets and
Religion, Trigonometry, Statistics*, Number and Patterns, Groups
and Finite Arithmetic*, Matrices,
Calculating Aids, Vectors, Graphset Algebra. * In
possession. Also see Edwards for other references in possession. Nothing of any
real interest here.
Jones, Owen. The Grammar of
Ornament. Studio Editions 1989. First published in 1856 (10 August 1993)
seen (or at least as recorded) in 8 October 1987, where I undertook extensive
studies of the day, albeit merely of ‘selective tracing’, and then larger, ‘freeform’
studies. As such, nothing remotely original emanated from this (a common
complaint for such book-based studies of the day).
As such, a glorious, sumptuous book, deserving of
greater study. ‘Paving of Diane’ Byzantine plate No. 3, Fig. 19. Also of note
is a reference to what has become known as a houndstooth pattern, p. 15, of
plaited straw from the Sandwich Islands. Lockwood and Macmillan in Geometric Symmetry, p. 90, refers to
this, although not referenced directly.
Judson, Horace Freeland. The Search for Solutions.
Hutchinson & Co. (Publishers) Ltd 1980 (28 February 2009).
General Science. See Chapter 2,
Pattern, in the broader sense.
Kappraff, Jay. Connections. The Geometric Bridge
Between Art and Science. McGraw-Hill Inc. 1991 (not date stamped)
Very nice indeed, full of
interest, although that said it largely repeats existing research. Especially
see Chapter 5, Tiling with Polygons. Many references and pictures relating to
Escher, pp. 71, 134, 191, 248, 265. Many chapters on polyhedra. Cairo tiling featured as
the dual of 32 .4. 3. 4, p. 181, although very carelessly drawn as
regards accuracy. has an excellent bibliography. I also have a later edition of
this book as a PDF, with minor extra material, with a supplement, and
Parquet deformation pp. 190-194,
within the chapter 5, Tilings with Polygons, albeit this merely excepted from
Huff’s article (1983), as the author credits. ‘Consternation’ is shown.
Kasner, Edward and James Newman. Mathematics and the
Imagination. G. Bell and Sons, Ltd. 1970 (25 April 1999) Simon and Shuster
1940. British edition first published 1949.
From Wikipedia: Mathematics
and the Imagination … hurtig
became a best-seller and received several glowing reviews. Special publicity
has been awarded it since it introduced the term googol for 10100,
and googolplex for 10googol. The book includes nine chapters, an
annotated bibliography of 45 titles, and an index in its 380 pages. … According
to I. Bernard Cohen, "it is the best account of modern mathematics
that we have", and is "written in a graceful style, combining clarity
of exposition with good humor". According to T. A. Ryan’s review, the book
"is not as superficial as one might expect a book at the popular level to
be. For instance, the description of the invention of the term googol…
is a very serious attempt to show how misused is the
term infinite when applied to large and finite numbers." By 1941
G. Waldo Dunnington could note the book had become a best-seller.
"Apparently it has succeeded in communicating to the layman something of
the pleasure experienced by the creative mathematician in difficult problem
Edward Kasner (April 2,
1878 – January 7, 1955) was a
prominent American mathematician who was appointed Tutor
on Mathematics in the Columbia University Mathematics Department.
Newman (1907–1966) was an American mathematician and
mathematical historian. He was also a lawyer, practicing in the state
of New York from 1929 to 1941. During and after World War II, he
held several positions in the United States government, including Chief
Intelligence Officer at the US Embassy in London, Special Assistant to
the Undersecretary of War, and Counsel to the US Senate Committee on
Atomic Energy. In the latter capacity, he helped to draft the Atomic
Energy Act of 1946. He became a member of the board of editors
for Scientific American beginning in 1948.
Popular account. Eminently
readable. Has many snippets of interest,
although no tessellation. Uses the term parhexagon pp 14-16. Space-filling
curves pp. 343-355. Chapter IV Assorted Geometries – Plane and Fancy predates
Frederickson’s use of the term.
Kay, Keith. Take A A Closer Look. Bright Intervals
Books 1991 (3 June 1993)
On optical illusions. Escher
tessellations Ascending and Descending,
s. 36 and Belvedere, p. 42. No text
worthy of the name. Also shows Otto van Eersel’s fish tessellation.
Keefe, John O’. and Phillip Rush. Weights and Measures.
Methuen and Co Ltd. 1966 (12 October 2002)
Kelsey, Kenneth and David King. The Ultimate Book of Number
Puzzles. Cresset 1992 (10 August 1993)
Kemp, Martin. The Science of Art. Optical Themes
in Western Art from Brunelleschi to Seurat. Yale University
Press New Haven
Second printing 1992.
A major work. As a broad statement, a series
on perspective, of notable substance. Much of interest and accessible. For eksempel,
Vredeman de Vries, p.111, with a possible source of Escher’s ‘Other World’. Dürer’s
geometrical designs, p.57. Many references to polyhedra, pp. 62-63. s. 159
shows two glass spheres, by J. M. W. Turner, with loose connection to Escher's Three Spheres II. Also has a substantial
section on colour, of which I had forgotten about….
However, although largely a
popular, albeit scholarly approach, much remains inaccessible, of which finding
aspects that I can understand amidst more weighty material is few and far
Kenney, Margaret J. and Stanley J. Bezuszka. Tessellations Using Logo
Dale Seymour Publications, 1987 (8 March 1995). Fra
Somewhat dated, with blocky
diagrams, likely as a consequent of Logo. Fused Cairo tile based on a square pp.
27-29. Has occasional ‘new’ tilings, such as p. 59, but not of any significance.
Alphabet tessellations (L, W, T), pp. 66-68 Islamic designs pp. 69-74. Chapter
on Escher type tessellation pp. 75-80 with ‘Fish’, Cat head, pecking pigeon,
frog tessellation of no particular merit. All in all the book is of no
Kepes, Gyorgy (ed). éducation
of Vision. Studio Vista, London (24 September 2017)
Chance purchase at car boot
sale. Broadly, on ‘basic design’, with 14 essays by the leading authorities in
the field. Most I am unfamiliar with, but of the few I recognise includes
Arnheim, Itten and Maldonaldo. However, there is next to nothing of any real
interest here; the book is most wordy indeed, and I simply don’t have the time
for an in-depth read, only skimming the pages.
P. 35 has a counterchange
reference (although of no consequence) by W. Turnbull, of London Central School
of Arts and Crafts. An admittedly brief look on Google for this proved
fruitless. I seem to recall having seen this elsewhere, although I am far from
I have no plans to re-visit
Kepler, Johannes. Harmony
of the World.
Available on-line from
Kepler Johannes. ils
Six-Cornered Snowflake. Oxford, UK: Clarendon Press, 1966. Trans. C.
Hardie. (September 2016)
Kim, Scott. Inversions.
W. H. Freeman and Company New York
1989. (30 April 1994)
Absolute delightful. Escher’s Sky and Water I p.112, commentary p.
113; Escher inversion p. 45. Parquet deformation pp. 14-15.
Kirkby, David and Peter Patilla. GCSE Maths Investigations. (7 May 1998, Hull)
A partial photocopy of
relevant pages of interest. Very minor tessellation.
King, Elspeth. People’s
Pictures: The story of tiles in Glasgow. Glasgow Museums 1991. PDF (13
Small booklet, of just 12
pages. Gives a history. No mathematical tiles as such. Of general interest.
Kinsey, L. Christine; Theresa E. Moore. Symmetry, Shape and Space with
Geometer’s Sketchpad. Student Lab Manual. Key College
Publishing 2004 (15 October 2009).
Tessellation pp. 57 onwards.
Klarner, David A. editor. The Mathematical Gardner. Wadsworth Inc.
1981 (24 March 2009)
A collection of articles in
honour of martin Gardner, with tiling featuring prominently. Especially see: In Praise of Amateurs, by Doris Schattschneider,
pp. 140-166 re Marjorie Rice and pentagons; Some
Problems on Plane Tilings, pp. 167-196, Branko Grünbaum; Angels and Devils.
H.S. M Coxeter. pp. 197-209. Escher references Colour plate IV, Coxeter article
s. 198 Angels and Devils, with typical Coxeteresque obscure text. Escher Sphere
with Fish p. 201. Polyhedron with Flowers, p. 202.
Kline, Morris. Mathematics. An Introduction to its Spirit
and Use. (Readings
from Scientific American). W. H. Freeman and Company 1979.
Chapter 3 has an extensive
series of articles by Martin Gardner of ‘geometric constructions’, from his
columns. (book not date stamped)
(Oddly, the front cover has a
Penrose tiling on the cover without any reference to this in the articles!).
————. Mathematics in Western Culture. The Scientific
Book Guild 1954 (30 July 2002).
Of limited interest.
Kneale, Nicholas. ils
Tile Book (Fired Earth). Printed by The Artisan Press Leicester,
June 1991 (14 September 1997)
Tile manufacturers’ 89 page catalogue/book
with various aspects of actual floor tiles. Of general interest, but nothing of
undue significance. Refers to a Mexican paver Saltillon p. 83 which I will
follow up. No Cairo.
Knox, Gerald M. (editor). Better
Homes and Gardens Treasury of Christmas Crafts and Foods. 1980, Meredith Corporation, Des Moines, Idaho pp. 6-7, 15, 19 (16 June 2014)
a crafts book, included here as it has a cluster puzzle reference, of a
nativity scene, apparently by David Ashe. However, there is no background
detail here at all. An open question is to whether this is the first recorded
instance of the type in print.
Knuth, Donald. The Art
of Computer Programming.
Volume 1 Fundamental Algorithms, Third Edition (Reading,
Massachusetts: Addison-Wesley, 1997), xx+650pp. ISBN 0-201-89683-4
Volume 3 Sorting and Searching, Second Edition (Reading,
Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout.
Grunbaum reference. High-end,
computer talk, way beyond my renter and understanding. Martin Gardner, Undiluted Hocus-Pocus also refers to
Knuth, p. 145-146, as to recreational elements, hence my latter day search for
Kordemsky, Boris A. (edited by Martin Gardner) The Moscow Puzzles.
Penguin Books 1976 First published in the United States and Canada 1972, and in
Russian, 1956 (9 October 1993)
style, and indeed most of the puzzles are derived from him. Occasional
dissections, no tessellation as such.
Kraitchik, Maurice. Mathematical Recreations. George
Allen & Unwin, Ltd. First published 1943 (18 March 2000, Lincoln). When first saw is unclear. Recorded
on a menu card is ‘Math Recreations College M. Kraitchik, again 17 September 1987’.
The first studies are dated 21 September 1987
Twelve chapters on various
aspects of recreational mathematics, with most of note Chapter 8, pp. 193-213 on tilings,
with: 1. on Geometric Recreations, 2. Mosaics, pp. 199-207. Also see 3. Mosaic
on the Sphere, pp. 208-209. Simple tiling diagrams, and ways of tiling with
various regular polygons in combination. Mention of MacMahon p. 53 as regards
Bachet. The preface mentions a French edition of sorts.
Laithwaite, Eric. Engineer
Through The Looking-Glass. British Broadcasting Corporation 1980. (11
October 1997, Lincoln)
Brief discussions on Mobius
band, flexagons and polyominoes. pp. -31;
————. An Inventor in
the Garden of Eden. Cambridge
University Press 1994 (22
Although more accurately a
general science book, it also contains occasional mathematics, hence its
placement here. See Von Koch snowflake curves pp. 23-25, Solid geometry pp.
91-94. Delightful reading. and worthy of a reread.
The Language of Mathematics. John Murray 1960 (21 June 1992)
Langdon, John. Wordplay. Bantam Press. 2005 (3 March
Delightful. Langdon can be described as a master of his craft. Escher pp. 170 Sky and Water I, 181 Angels
Langdon, Nigel and Janet Cook. Introduction to Maths.
Usborne Publishing Limited 1984 (16 July 1994).
Juvenile. Usage is made of
Escher’s Swans tessellation, p. 13, but without detail or credit!
Langdon, Nigel et
Charles Snape. A way with maths Cambridge University Press, 1984, 48 pages,
juvenile. (First saw, or at least recorded date of study 15 July 1988)
Of note is a tessellation section, of an Islamic tiling, pentagons and Escher-like, not all of which I
photocopied, with only p. 19 so copied.
Langdon, John. Practise Your
Calculator Skills. Usborne. 1983 (20 July 199** – year has faded)
Larcher, Jean. Allover Patterns With Letter Forms.
Dover Publications, Inc. 1985. (22 September 1993)
More inclined to pattern per
se (with letters) than tessellation. The book lacks structure, seemingly of an
ad hoc arrangement of letters (albeit of all the alphabet) in a symmetrical
arrangement. Of limited interest.
Large, Tori. ils
Usborne Illustrated Dictionary of Maths. Usborne Publishing Limited, first
published 2003. (16 May 2015)
Ostensibly for a juvenile
audience, although some parts are decidedly advanced! 500 maths terms are
explained, of which frequently served as a refresher for me. Has an extensive
chapter on Shapes, space and measures , with tessellation featuring, p.36,
although only of regular and semi regular tessellations. No Escher aspect.
Lasker, Edward. Go and
Go-Moku the Oriental Board Games. Dover Publications Inc., Second revised
edition 1960 (of a 1934 work) (23 August 1992)
Popular account. Never played
the game though! Got on general interest.
Last, Derick (ed.) The Art Machine Pattern Book. Leapfrogs
1990. (30 April 1994).
Of interest is a Cairo pentagon-esque in
combination with a kite, p. 5. Many computer drawn examples, badly dated. Tiling
pp. 49-51, 54, the latter of Escher-like ‘gnomes’, by Richard Ladds.
Lanz, Sherlee. Trianglepoint. From Persian Pavilions to Op
Art with One Stitch. The Viking Press 1976 (28 June 1998)
From a reference in Grünbaum.
All of a triangular premise. Has many pleasing tessellation aspects throughout.
Of note a truncated houndstooth tiling, titled ‘snowcaps’ colour plate 29 and p.
96 where it is stated ‘woven shawl, nineteenth century, the Sandwich Islands’,
which I have seen quoted elsewhere.
Lea, Derek. Creative
Photoshop. Digital Illustration and Art Techniques. Focal Press, 2007 (c.
Strictly a book on Photoshop
rather than mathematics per se, and so its listing here is perhaps somewhat
questionable. However, it justifies its inclusion here as it contains a
tutorial on a composition based on Escher's premises of Bond of Union, page 195 and (primarily) Sky and Water I, pp. 340-349, and so I thus include here for the
sake of convenience.
Leapfrogs 1982. Tarquin Publications (26 March 1994)
Leapfrogs. Poster notes. Tarquin Publications not
dated (3 June 1993)
Some tessellation but treated
in a lightweight manner. Written in conjunction with a series of posters produced
Lemon, Don. Everybody’s
Illustrated Book of Puzzles. London, Saxon and Co, 1890 PDF (Downloaded from
internet 10 June 2014)
From a reference on Rob Steggman’s
site. 794 puzzles. Very much alike in style to Dudeney’s later works. si
Dudeney was aware, or was influenced remains conjecture; in his books he does
not give a bibliography. Various geometric puzzles and dissections, pp. 8,
11-12, 35, 40, 46, 51, 55, 63, 67, 69, 77, 89. No tessellation or polyhedra.
Lewis, Donald J. Introduction to Algebra. Harper and
Row. 1965 (29 May 1994)
Academic. Illustrated with Escher’s
prints: Cover, Preface, Three Spheres; introduction, Puddle Chapter
2, p.26 Three Worlds; Chapter 3, p. 77 métamorphose, Chapter 4,
s. 138, Relativity; Chapter 5 p. 232, Reptiles.
Levy Joel? optique
Illusions. Dorling Kindersley Limited 2012. (30 May 2016)
A nicely produced book, of
school-age level, of interactive nature, with various paper engineering
pop-ups. However, there is nothing new or innovative here; it consists of
illusions that are already known. Of perhaps most interest is that of the ‘Get
of the Earth Puzzle’, p. 28, of which I have seen but not actually have a
workable model to hand until now.
that I am unsure of the author; a whole list of people are given, of which who
is most associated with the book is unclear. Joel is given above as ‘most
likely’, albeit with the above in mind.
Lewis, K. Polyhedra. Further Experiments in
Mathematics. Book 2. Longmans, Green and Co Ltd 1969. (24 October 1998).
Juvenile, but still of
Jean. Récréation Mathématique. aucun
publisher. 1624 (Downloaded from Internet 7 May 2015). 200 pages
From a reference in MacMahon. No tiling or polyhedra.
Occasional geometry, pp. 38-39 (58-59) and 73 (93). Mostly text, although
indeed with many diagrams. Note that there is considerable debate at authorship
of his book (see Singmaster), of which in itself is of historical importance,
it being the first bearing the title of ‘recreational mathematics’. Albrecht
Heeffer has written a scholarly article on this.
Libbrecht, Kenneth. ils
Snowflake Winter’s Secret Beauty. Colin Baxter Photography Ltd, 2004. First
published 2003, US (22 May 2016)
Popular account, from a
Licks, H. E. Recreations
in Mathematics. D. Van Nostrand Company, Inc. second printing 1916 PDF ((Downloaded from Internet 14 July 2014)
From a reference in Stegmann’s
site. 15 puzzle pp. 20-21; magic squares pp. 39-43, geometric fallacies pp. 54-55,
map colouring pp. 61-62, bees speculations pp. 91-99, 155 pages.
Liebeck, Pamela. How Children Learn Mathematics.
Penguin Books 1988 (16 February 1995)
pp. 118-119 (includes a fish of no great merit). Basic, as to be expected.
Lindgren, Harry. Recreational Problems in Geometric
Dissections & How to Solve Them. Revised and Enlarged by Greg
Frederickson. Dover Publications, Inc. New
York 1972. Originally published in 1964 as Geometric Dissections (1 September 1995)
Delightful! I went thorough
the book at date unknown looking for anything ‘Cairo-like’, or of a par
hexagon. As such, nothing. That said, a diagram on p 105 could have been made
into a Cairo
Livio, Mario. ils
Golden Ratio. Review, 2003, first published in 2002. (12 April 2014)
Much of interest (and
accessible) throughout the book, but especially see re tiling Chapter 8, pp.
201-228 ‘ From the Tiles to the Heavens’
Escher p. 203, Penrose tiling pp.
Note that the Livio here is
not the same as a namesake, Livio Zuccha of tiling fame; it’s easy to mix them
vers le haut.
Locher, J. L. (general editor). Escher The Complete
Graphic Work. Thames and Hudson 1992. (9 April 1993). Note that this
is an English edition translated (by Tony Langham and Plymm Peters) from the
original Dutch Leven en Werk von M. C.
Escher of 1981
Indispensable! One of the core
books on Escher. Includes essays by M. C. Escher, with five joint author
credits: F. H. Bool, Bruno Ernst, J. R. Kist, J. L. Locher and F. Wierda.
Locher wrote the preface. However, the rest of the text is a combined effort;
whether any one author is leading is not stated. Although not given as
chapters, twelve can be identified, along with an extensive catalogue (the main
part of the book) complied by F. H. Bool, J. Locher and F. Wierda. Invaluable
are the ‘notes on illustrations’, pp. 329-343. Includes a one-page ‘selected
bibliography’, p. 345, with misspelling of Maas. And to think I waited until
1993 to obtain this!
————. The World of M. C. Escher. Abradale Press Harry
N. Abrams Publishers Inc. New York 1988 (9 April 1993) First Published 1971
Another core value book,
indispensable. Has five essays: The World of M. C. Escher, J. L. Locher;
Escher: Science and Fiction, C. H. A Broos, Approaches to Infinity, M.C.
Escher. Structural Sensation G. W .Locher, The Mathematical Implications of
Escher’s Prints. H. S. M. Coxeter, and a catalogue of the more important prints.
Includes a excellent selected three-page bibliography, pp. 57-59, with
misspelling of Maas.
————. The Infinite World of M. C. Escher. Abradale
Press/Harry N. Abrams Inc. New York First published 1984 (First saw c. 14
December 1987) In possession 10 April 2018
The book is described as:
‘This 1984 edition is published by Harry
N. Abrams Inc. New York. It is a concise edition of Abrams’ The World of M.C.
Escher, originally published in 1972…’. 151 pp as against 263 pp. Tihis concise
edition has only two of the five essays of the earlier book (‘The work of M.C.
Escher’ and ‘Approaches to Infinity’). It also lacks the ‘Selected Bibliography’
and ‘Exhibitions and Lectures’. Most of the plates are retained, albeit with
liten rearrangements. The colour plates remain the same. As such, I see little merit to this concise utgave; there is nothing new here. indeed, with The World en min besittelse, I saw little need to målrettet pursue this i ettertid. however, upon gjennomgå (2018), it became highly souhaitable, to refer page numbers
and to check which exactly of the
prints were shown, and so as it was disponible at a respectable price (£3.69) I decided to obtain.
Locher, P. and C. Nodine. ‘The Perceptual value of symmetry.
Computers and Mathematics With Applications 17, 4-6 475-484, 1989
From a Craig Kaplan thesis
Locke, John. Isometric Perspective Designs and How to
Create Them. Dover Publications, Inc. 1981. (22 September 1993)
Lockwood, E. H. A Book of
Curves. Cambridge University Press 1963 (first printed 1961) (not date
A delightful book, although
much is beyond my understanding. Gives history as well. One of the first books
I ‘studied’, in 1987, from the college library. Quite when I later obtained it
is decidedly unclear; I neglected to date stamp. At a guess, 1998, albeit with
a five year leeway either side!
Lockwood, E. H. and R. H. Macmillan. Geometric symmetry. Cambridge
University Press 1978,
2008. (21 December 2010)
Largely of an academic nature.
reference p. 88. Escher p. 4, Shells and Starfish, E42, Fish E41, p. 66
Lizards, E56. Shows a houndstooth design p. 90 (on a small piece on making automatic reproductions), and of which although claiming to be from the Sandwich Islands (clearly derived from Owen Jones' account, with plaited straw) is not strictly so. Rather, for unclear reasons, this is a variation, indeed interesting in itself, but is not directly based on the Jones diagram.
Lodding, Ken. Byte.
The small systems journal. 1979 Volume 4 No. 2 (February) 21 September
‘Escher inspiration’ on cover,
of ‘Drawing Hands’, with minor acknowledgement to Escher pp. 3-4.
Logi, Angiolo. Text by Daniele Ravenna editorial coordinator
Linda Fox. Australia Puzzle. Contemporary
Silverware & Jewellery. Puzzle Pty Ltd 1994 (19 November 2016)
Gift of Lorenzo Logi. beaucoup
instances of cluster puzzles: pp 10-11 (the Discovery of Australia) The First
Black Swan pp14-15; The Southern Cross pp.16-17; Escher mention c. 20. The
Dreaming (Gatefold pull-out); Australian Land and Seas (1986); The Japan Puzzle
(1989) pp. 42-43; Stevie Wonder with Australia Puzzle p. 54.
Loeb, Arthur, L. Color and Symmetry. Robert E.
Krieger Publishing Company. Huntingdon,
New York reprint 1978 (the
original edition is 1971)
Occasional reference to
Escher: pp. 65-66, 79, 102, 119-120, 162-169. Pictures include p. 66 Horseman,
s. 120 Running man, p.163 Fish, p. 164 Lizards, p. 166 Butterflies.
————. Concepts &
photos Visual Mathematics. Design
Science Collection. Birkhäuser Boston 1993. (9 October 2014)
Found upon a Google book
search, upon which I noticed some pentagon studies. Especially see Chapter 9, pp.
89-100 ‘Pentagonal Tessellations’, featuring a unaccredited Cairo tiling, and
Chapter 10 pp. 101-105, ‘Hexagonal Tessellations’. Largely, save for the
pentagon chapter in particular, the book is a disappointment, the concepts are too
difficult for me to follow.
Loon, Borin van. Geodesic
Domes. Tarquin Publications 1994 (30 April 1994)
Of peripheral interest. ils
book has cut out nets to assemble, but not undertaken. Commentary is given as
to the domes.
Love, Brian. Play the
Game. Book Club Associates, 1978. (29 January 2014)
Included despite there
strictly being no mathematics here whatsoever. General board games of
yesteryear, with each game over a two-page spread. Oversize. Checked for any
jigsaw type puzzles/games but there are none.
Loveridge, Emma. Egypt.
Country Fact Files. Macdonald Young Books, first published 1997. Children’s
book (22 June 2014. First saw in Cleethorpes library c. 2013)
Although not a maths book per
se, included as it has a picture of the Cairo tiling. Cairo tiling photo at the Old Cataract hotel
pp. 8-9. However, this is only recognised with foreknowledge, as the picture is from afar
that without cognizance of the tiling would otherwise pass unnoticed. ils
photographer credit is ‘The Image Bank, Kodansha Images’, but upon searching I
could find no reference to the picture here.
Loyd, Sam (Jr). Sam
Loyd’s Cyclopedia of 5000 Tricks and Puzzles. New York. The Lamb Publishing
Company 1914 PDF (17 May)
As compiled by his son, Sam.
Impressive, even when due allowance is made for unaccredited borrowing from
Dudeney. However, the book is not without fault. Gardner states (in Mathematical Puzzles of Sam Loyd) it is
‘riddled with mistakes, typographical errors, wrong answers and frequently no
answers at all’. No tessellation of any note.
Lukas, Edouard. L’Arithmétique
Amusante. In French, 1895. Gauthier Villars et fils, France PDF (25 June
From a reference in MacMahon
(and others). As found on Rob Steggmann’s site. Nothing on tessellation,
polyhedra and the barest minimum on geometry. Lots of playing card recreations.
Luckiesh, M. Visual Illusions. Their Causes,
Characteristics & Applications. Dover
publications Inc., New York
1965. Introduction to Dover edition by William H. Ittelson, 1965. Originally
1920 (18 September 1995)
Although strictly not a book
on mathematics, included as it has certain crossovers. Maple leaf tessellation
p.65, with a chapter on equivocal figures. Much of interest in a generalised
MacGillavry, C. H. Symmetry Aspects of M. C. Escher's
Periodic Drawings. Oosthoek, Utrecht
1965. (Reprinted as Fantasy & Symmetry. The Periodic Drawings of M. C.
Escher. Harry N. Abrams, New York
1976.) (First saw April 1988 and again 18 August 2003)
41 plates of Escher
tessellations, 12 in colour. Each plate is accompanied by text, with a
crystallographic premise (this being MacGillavry’s background). Although these
are broadly ‘readable’, the analysis strays into abstruse discussions, way
beyond what Escher had in mind, and so consequently is of limited interest.
Escher also wrote the preface. Many of the tessellations were not previously
published of the day, but the book has since been put in the shade in this
regard by Schattsneider’s inclusion of all the periodic drawings, in Visions of Symmetry of 1990.
MacMahon, P. A. New Mathematical Pastimes. Cambridge University Press 1921 and 1930.
(Reprinted by Tarquin Books 2004) (31 March 2005)
Most impressive. Has
considerable tessellation interest. Cairo
diagram (but obviously not attributed) page 101, the first (1921) recorded
instance in a book or article? (Moore's patent predates this). The only possible
precursor to this is Haag (1911), as the others in Schattschneider’s list i.e.
Laves et al are all after 1921.
Madachy, Joseph S. Madachy’s Mathematical Recreations. Dover
Publications Inc, New York.
1979 (10 August 2006). Note that this is a re-titling of Mathematics on Vacation, Charles
Scribner’s Sons, 1966, unabridged, with corrections
First, note the title change
as above. Originally saw this (Mathematics
on Vacation) in College library (and ‘studied’, or at least first recorded broadly
stated in October 1987), but only in 2006 did I obtain. Of most interest is
Chapter 1, Geometric Dissections pp. 15-33. Chapter 3, Fun with paper pp.
55-84, on flexagons. As such, the material is derived from Madachy’s Journal of Recreational Mathematics Magazine
P. 8 states ‘Much of the material is taken from Recreational Mathematics Magazine (of 1960-1964). Upon an initial
glance through the book, there is nothing original here; the material appears
to have been taken from existing sources.
Malone, Maggie. 120 Patterns
for Traditional Patchwork Quilts. Likely Published by HarperCollins
Distribution Services 1983. NOT IN POSSESSION, FIRST RECORDED STUDY OF 2 July
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed led to extensive studies of the day
(1987), as indeed with other patchwork books). However, now, and for some
considerable time, the nature of the material is considered hardly worthy of the
time originally devoted to it. note that Malone has published a whole series of
books of numbered titles, with 115, 500, 1001 patterns, of which I only have
the latter. Investigating the others seems hardly worth the bother.
Malone, Maggie. 1001
Patchwork Designs. Sterling Publishing Co Inc, New York 1982 (28 August
Essentially an illustrative
book, with any text at a premium. Note that the 1001 designs are not discussed
Mallinson, Phillip R. Geometry
& its Applications Tessellations.
Comap, 1996. (?) PDF
Note that I have this as a PDF
rather than a book. Cairo tiling p. 17.
Mankiewicz, Richard. ils
Story of Mathematics. Cassell & Co 2000 (Grimsby Library). (c. 2011)
Escher, pp. 6, p. 125 Circle
Limit IV, p.129 Mobius Strip II .
Maor, Eli. To Infinity and Beyond. A Cultural History of
the Infinite. Princeton
University Press 1991 (Grimsby Library).
Has tessellation articles:
Tiling the Plane, pp. 102-106, which contains a Cairo diagram, albeit not
original, the diagram taken from O’Daffer and Clements, and Maurits C. Escher –
Master of the Infinite, pp.164-178 (16 October 2010).
Mandelbrot, Benoit B. Fractals:
Form, Chance and Dimension. W. H. Freeman
& Co Ltd, 1977. First saw Grimsby library 11 May 1991
365 pp. From a reference on an
old cardboard ring binder with a Grimsby Central library reference. ils
reference also mentioned the similarity of a hexagon to the outline of France. Je
now (2018) do not recall anything from this book. As such, it was likely seen
out of possible interest in and nothing more. Certainly, no studies have
emanated from it. I am not actively going to pursue this.
————. The Fractal Geometry
of Nature. (updated and augmented) W. H. Freeman and Company, 1983? (10
October 2016). PDF.
A weighty tome of 468 pages. Je
have seen occasional references to this, although Escher and tessellation are
mentioned essentially in passing, in regard of hyperbolic geometry, pp. 23, pp.
158-169, and bibliography.
The nature of an electronic
copy prevents a pleasant reading, of which I have looked at just the first few
Marjoram, D. T. E. Exercises in Modern Mathematics.
Pergamon Press 1975 (18 September 1988?)
The only interest is in
Chapter 10, Topology.
Holt, Michael and D. T. E. Marjoram. Mathematics Through Experience. Seemingly a five book series. 2 HarperCollins
Distribution Services (March 1966
First seen, or at least recorded
on a shared sheet of many different studies. E. H. Lockwood describes this as of
CSE level, which book I saw is uncertain. A henvisning gives ‘No. 3’, but this may
be association with a page number of the book to hand, not necessarily of Book
Marks, Robert W. The New Mathematics Dictionary and
Håndbok. Bantam Books 1967 (9 April 2007)
No entries for ‘Tessellation’
or ‘Tiling’! Be that as it may, still a handy reference guide.
Martin, George E. Polyominoes. A Guide to Puzzles and
Problems in Tiling. Mathematical Association of America. 1991 (2 February 1998)
A general overview of the
subject, with questions. Mostly of a popular level. Brief discussion on the
Penrose loaded wheelbarrow p. 165, pp. 170-171.
Maxwell, E. A. Geometry For Advanced Pupils. Oxford at the Clarendon
Press, 1966. First edition 1949 (11 October 1997)
Advanced it is indeed, of
which despite claiming to be aimed at écoles,
is more properly described of a university level! Unfortunately it is far too
advanced for me, of no practical use. Note that this is not a text book as such,
in the spirit of Euclid, but rather a series of various aspects of Geometry,
such as theorems of Menelaus and Ceva, to give an arbitrary instance.
McCann, Chris. Master
Pieces: The Art History of Jigsaw Puzzles. Published by Collectors Press,
Inc., 1998 (24 February 2017)
Although not a maths book,
included as regards my jigsaw puzzle interest as I have seen this book quoted
in various ‘serious’ jigsaw books, I obtained on the off chance that it may be
useful to me in some way. However, as such, it is a relative disappointment, at
least to my special interests in the field, although I was indeed prepared for
this, given the title as the book is faktisk
subtitled, this is of art history aspect of jigsaws, with biographies, and so
there is indeed relatively little on jigsaws per se (Tuco is the best, p. 197,
his special interest); certainly nothing on cluster puzzles! (or indeed any
type of ‘innovation’). Williams critiques this (GRN?) for generally lacking the
puzzle manufacturers names, of which I concur. Although occasionally some of
the manufacturers are indeed mentioned, this is most scanty. The book also
lacks an index. However, one should not perhaps be too critical here, as the
title admirably describes the book! It is not McCann’s fault that our
respective interests are different. Même si
there is nothing of direct interest, there might have been, and so the matter
is settled conclusively.
McCartin, Brian J. Mysteries of the Equilateral Triangle.
Hikari Ltd 2012
McCleay, Heather. The Knots Puzzle Book. Tarquin
Publications 1994 (7 November 1998)
McCloud, Scott. Understanding
Comics. HarperCollins, 1993 (2009)
From a reference in Craig
Kaplan’s thesis. Has many salient point indirectly as to Escher-like
McCormack, Tony. Driveways,
Paths and Patios. A Complete Guide to Design, Management and Construction.
The Crowood Press Ltd, 2005. (2 July 2016, Cleethorpes library)
On in situ paving (having
previously seen his most informatif et interessant website on paving). Mostly of background matters as to the intricacies
of paving; as such, there is next to nothing on pattern in the broad sense. de
little to no interest mathematically.
McGary, Debi. Herlig
Wood Puzzles. Plaid Enterprises Inc, Norcross, GA 1996
NOT IN POSSESSION
Although not a maths book,
included as regards my cluster puzzle interest. Anne Williams reference.
Six wood-themed cluster-type
puzzles, with the veracity varying considerably, from true tessellation to
considerable vacant regions. Her work is inconsequential. McGary is oddly
anonymous on the web.
McGregor, Jim and Alan Watt. ils Art of Microcomputer
Graphics for the BBC
Micro/Electron (First saw college library 1987 (the day and month are
uncertain, with the earliest reference being 24 January) Addison Wesley 1994
Despite being a book
ostensibly on ‘microcomputer graphics’, it has notable tessellation aspects,
and so hence my interest in it of the day. The book is notable for its
plagiarism of Martin Gardner, with verbatim text.
Specific aspects of interest
include: Chapter 5 Night and day – a journey through the world of tesselations (tesselations as spelt as in original)
Cairo pentagon references: text, p. 196, and picture, p. 197
Illustrated with a line drawing. (and p. 208?)
Text: ‘An example of a
pentagon that will tesselate (sic) is the well-known Cairo tile, so called
because many of the streets were paved in this pattern (Figure 5.2). The Cairo tile is equilateral
but not regular because its angles are not the same’.
Moore pentagon, p. 198.
McLeish, John. Number. From cave people to computers, a
revolutionary view of ourselves. Bloomsbury
Publishing Limited, 1991 (17 December 2005)
Historical account. 18
Chapters. Of little direct interest.
McMorris, Penny. Quilting. An Introduction to American
Patchwork Design. British Broadcasting Corporation. First Published in
1981, US. UK edition with revisions first published in 1984 (13 October 2001)
First saw c. 1987
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and led to minor studies (a dual sided sheet) of
the day (1987), as indeed with other patchwork books. However, now, and for
some considerable time, the nature of the material is considered hardly worthy
the time originally devoted to it.
Meehan, Adrian. Celtic Design. Animal Patterns. Thames and Hudson
1995 (7 March 2009)
‘How to…’ book.
Meer, Ron van der. ils
Ultimate 3-D Pop-up Art Book. Dorling Kindersley, 1997. Originally
published by Van der Meer publishing, 1995 (7 June 2014)
Although not a maths book per
se, included as it has a Escher reference, of fish and frogs periodic drawing;
pages are not listed. Many pages are of interest in a generalised sense, with
aspects of ‘scientific art’.
Menkhoff, Inga. optique
Illusions. Amazing Deceptive Images – Where Seeing is Believing. Paragon
Books Ltd 2007 (1 May 2011)
‘Ascending and Descending’ and
‘Relativity’, pp. 92-93. Minor text.
Meyer, Franz Sales. Handbook of Ornament. Dover Pub. Inc. 1957. First
edition 1888 (30 October 1993, Sheffield)
first saw 23 June 1990
The book is rather of ornament
in its many forms rather than tessellations. However, there are indeed tilings
here, notably pp. 10-12, albeit simple, of an arbitrary nature without
structure. Of note in particular is of plate 6, diagram 11. This can be seen to
be the same tiling as of Pólya’s Do3 diagram, and so predates this. Also, pp. 279-280.
Michell, George. ils
Majesty of Mughal Decoration. The Art and Architecture of Islamic India. Thames & Hudson, 2007. (7 September 2018)
Oversize coffee table book. Purchased
for a specific reason. Upon a (2018) reading of a 17th century Cairo tile
Mughal jali reference in Simon Ray’s Islamic catalogue of 2016, in which this
book, being the sole quoted reference, appears to be the source. However, I find
that this is not so; it is not in the book! A major disappointment in this regard, to mettre la
mildly. However, there is at least an interesting chapter on Geometry, pp.
68-107, that discusses tilings. Also see Jan Pieper and George Michell for more
Michell was a new name to me,
although I see that upon a coincidental contemporary chance revisit to Craig
Kaplan’s thesis he gets a sideways mention, p. 206, reference 98.
Midonick, Henrietta. The Treasury of Mathematics: 2. A Collection of Source Material in
Mathematics Edited and Presented with Introductory Biographical and Historical
Sketches. First published in the USA 1965. Penguin Books 1965 (29 October
Small format paperback, 416
pp. In four sections: Further Development, Algebraic Geometry and Calculus,
Logic, Modern Algebra.
Select text from eksisterende works. 24 biographies on ‘the greats’. Most of this is way beyond my
understanding. Largely accessible is Albrecht Durer, pp. 104-122. Useful for
reference purposes, but nothing more. I have no plans to re-read.
Miller, Charles D., Vern E Heeren, John E. Hornsby, Jr. matematisk
Ideas. Sixth Edition. HarperCollins publishers 1990. (22 July 199? Last
number missed; 1998?)
Generally advanced maths,
occasional recreational aspects, such as mathematics on stamps liberally
throughout the book. Potted biographies of mathematicians liberally sprinkled
throughout. No tiling as such. Chapter 9 on geometry.
Millington, Roger. The Strange World of the Crossword
Puzzle. M & J Hobbs in association with Michael Joseph. 1974 (5 October
‘Cairo crossword’ puzzle, by ‘Croton’, from The Listener pp. 100 and 175 (solution),
but without further detail. April 2012 research dates this as of 1951 and (not
shown) 1954, and so of considerable historical significance. Also see this
repeated in Investigation in Mathematics
by L. Mottershead, but only indirectly credited.
Mirrow, Gregory. A
Treasury of Design for Artists and Craftsmen. 725 paisleys, florals,
geometrics, folk & primitive motifs. Dover Publications Inc, 1969 (4
Free, charity shop. Dover pictorial
series, and as in the title, of a pictorial nature, without any explanatory
text save for the back cover. In five sections, as according to the categories
above. Of most interest is geometrics, and in particular a joined/seamless
houndstooth, p. 53, that will be studied. Otherwise, there is nothing particularly
new or innovative.
Mitchell, James (general editor). Science and the Universe. Mitchell Beazley 1977.
Minor reference to Escher’s prints
Angels and Devils, p. 51 and Mobius band, p. 53, with general comment. puis
lightweight as be barely worth comment.
Mold, Josephine. Circles. Topics From Mathematics. Cambridge University Press 1967. (20 August 2000?)
This book is one of a six-part
series from ‘Topics of Mathematics’,
three of which are by Mold (Solid Models,
Circles et Tessellations) and three by David S. Fielker (Cubes, Computers et Statisitics). All are of a like
presentation and page range of 31-32 pages, from 1967 onwards. Circles et Tessellations are the only ones in possession.
Small, 32-page booklet, for barn. Very accessible, with much of interest.
————. Tessellations. Topics From Mathematics.
Cambridge University Press 1969 (20 February 1991) photocopied book
School age level, but still of
interest. Shows dual Archimedean tiling, p. 25, which can be interpreted as Cairo. Also interesting
fish tiling that has dual properties, possibly as a by-product of drawing,
rather than purposefully so.
Also of note, as regards
Robert Ferréol’s interest in examples of Pavage de Diane, is p. 17, where there
is a report of this as an in situ tiling ‘… on the floor of an old shop in
Windsor’, with a side reference to Windsor Castle. Upon an initial look, this
was not, unsurprisingly, found.
Montrose, Clifford. jeu
To Play By Yourself. Suitable for young and old a boon to the convalescent.
London: Universal Publications Ltd. No date of publication, but given online as
1935, 1936, 1937 (not date stamped, c. 1997 + – 5 years)
Small format paperback, of 90
pages. Stated of a variety of indoor games that you can play alone. Nothing of
an overt geometrical nature. Includes: Solitaire pp. 16-19, The Wonderful
Puzzle Fifteen pp. 41-43. One of many of its type, with no plans for a
Moon, Brian. Literary
Terms: A Practical Glossary. The English & Media Centre. First
published in Australia
1992. (English publication date not stated) (5 November 2011)
Note that although this book
is not mathematical, I have decided to include it here in this listing, as it uses
Escher's print ‘Drawing Hands’ on the cover, and so is of interest in that regard.
Moore, Alison (ed.) Reader’s Digest Compendium of Puzzles
& Brain Teasers. The Reader’s Digest Association Limited 2000 (14 July
Escher’s Relativity s.
55, with minor text barely worth the mention.
Morgan, Bryan. Men and Discoveries in Mathematics.
John Murray, 1972 (24 October 1998)
Poplar account, from over
5,000 years to today. The discussion is in general terms, rather than focusing
on specific individuals as an in-depth detail.
Morgan, W; Pickering, J. R. Mathematics I et II Sir Isaac Pitman &
Sons, Ltd. 1946 and 1948. 19 July 1992
Textbook, typical of the day,
with many problems in calculation, of little interest.
Morris, I. H. and Joseph
Mari. Practical Plane and Solid Geometry. Longman, Green and Co. 1944
(26 March 1994, Scunthorpe)
Typical generic geometry text
book of the day, one of many that I have; simply, one would have sufficed. ils
reason for obtaining the book was to be able to look up any geometric
construction as and if required, but I do not believe that I have used this in
any way. Pattern p.116, tracery p.117.
Moscovich, Ivan. Mind
Benders. Games of Chance. Penguin Books 1986. (13 June 1999)
————. Mind Benders. Games of Shape. Penguin Books
1986. (5 July 1998)
————. Ivan Moscovich’s Super-Games. Hutchinson & Co.
1984 (28 November 2004)
consultant editor Ian Stewart.
Various Dudeneyesque puzzles
of a one-two page per entry nature, 59 distinct entries, some original,
although which is which is not made clear. Lavishly illustrated. aucun
tessellation as such, although plenty of off-shoots.
Mirror & Other Puzzles. BCA. 2005 (2 May 2009)
The book is of a series of 12
(four of which I have) published under the generic theme of ‘Ivan Moscovich’s
Mastermind Collection’. c. 100 aspects of ‘simple’ recreational mathematics,
pitched at a juvenile level, mostly seen before but nonetheless remain of
interest. given such a large number fully documenting the books is
problematical, and so I thus outline aspects of immediate interest only. ils
title given is apparently chosen arbitrarily by Moscovich, given that each
puzzle is discussed over one or two pages.
No tessellation. Dissection p.
27, packing discs or circles, pp. 36-45.
————. The Hinged
Torget & Other Puzzles BCA. 2005
(2 May 2009).
Somewhat disarmingly here, p.
76, on the golden ratio propagates (or at least seems to imply) the ‘belly
————. The Shoelace
Problem & Other Puzzles BCA.
2005 (2 May 2009)
————. The Monty Hall Problem. & Other Puzzles BCA. 2005 (2 May 2009)
————. Loopy Logic
Problems & Other Puzzles (31 July 2013)
Sterling Publishing Co, Inc, New York, 2006
Moser, Koloman. Turn of the Century Viennese Patterns and
Designs. Dover Publications Inc. Mineola,
New York 1998 (6 August 2010). New
introduction by Leonard Fox and Mark Weinbaum.
Dover states that this: ‘is a
republication of all the plates included in the portfolio Flächenschmuck, from the Moser Issue of Die Quelle, published in Vienna and Liepzig by Verlag M. Gerlach,
Historically significant, as
here are the first true life-like
Escher tessellations (I do not consider the ‘Peru’ types bona fide examples). However, separating
‘design’ from tessellation here is fraught with difficulty; there is a definite
blurring. The tessellations are not always of a ‘no gaps’ premise. Clearly identifiable as life-like
tilings: p.12 (human figure), p. 25 (birds), p. 37 (goldfish), p. 48 (birds),
s. 53 (woman), p.57 (woman, with gaps). Birds of p. 25 is noticeably favoured
for true premise and inherent quality.
Lorraine. Sources of
Mathematical Discovery. Basil Blackwell 1977. (8 March 1997)
A delightful book, albeit with
much plagiarism, with much of interest, with a recreational promise, and in
particular a unit (chapter) on tessellations. Escher pages: 39, 110, 112-114,
163-166. Horseman, 113; Sky and Water I, 113; Reptiles, 114; Relativity, 163;
Waterfall, 164; Belvedere 165; Ascending and Descending 166.
This also features the Cairo tile pp. 106-107 in
a section on irregular pentagons. This is also shown as cells in a crossword
puzzle. Curiously, Mottershead mentions ‘Croton’ (i. e. the compiler in The Listener!) in association with ‘her’
page of Cairo
puzzles! Previously (prior to 2 April 2012), I thought these were original with
her, but apparently not! However, to give credit to her, she does indeed
mention ‘Croton’ on the page.
cover has an op art design apparently attributed to one Chris Belson. Les propriétaires étaient
he is not the designer! Carraher and Thurston in Optical Illusions and the Visual Arts (1966), page 59, reproduce
this design, with credit given to Franco Grignani.
Of note is that Mottershead
shamefully appropriates (1963) Gettings’ diagrams in The Meaning and Magic of Art s. 64 on see p. 128 of Sources…’
without any mention of Gettings!
The first of two books of a
like nature by Mottershead, although wide apart in chronology, namely of 1977 and 1985.
————. Investigations in Mathematics. Basil Blackwell
1985. (8 March 1997)
No Escher references or
pictures. The book consists of 6 units, or chapters. As with Mottershead’s
earlier book, this is very much in the same vein, of a recreational nature.
however, here, as an observation, more on numbers, rather than symmetry matters
of the other book. That said, there is indeed tilings here, and indeed, this
was studied in 1987 (at Grimsby reference library).
Mott-Smith, Geoffrey. matematisk
Puzzles, for Beginners and Enthusiasts. Volume 106 of New home library.
Blakiston Company, 1946. Reprinted by Dover Publications, New York, 1954 WANTED
Has geometric dissections p.
————. The Handy Book of Indoor Games. Garden City
Publishing Co, Inc. Permabooks. 1949. (Not
date stamped, c. 1997, + – five years)
Small format hardbook, 245
pages. In three parts: 1. Card Games, 2.
Board and Piece Games, and 3. Word Games and Pencil-and-Paper Games. The main
essence is on card games. Only of minor passing
interest, with nothing really in my field. Note that Mott-Smith was a geometric
disseksjon enthusiast, and is discussed in Frederickson, Plane and Fancy, with a biography p. 111, but there is nothing in
this line in the book.
Munari, Bruno. Design as Art. Penguin Books Ltd 1971 (Not
date stamped, c 2006, at a guess)
On design, rather than maths.
Occasional mathematics. Note that Munari is an associate of Mari.
Murphy, Lawrence R. ils
American University in Cairo: 1918-1987. The American University
in Cairo Press,
1987 (9 August 2012)
Although not a mathematics
book per se, as it contains incidental instances of the Cairo tile, pp. 64 and 254 (the best picture),
I thus include here. A picture of uncertainty is p. 175, possibly of the square
Murphy, Patrick. Modern Mathematics Made Simple.
Heinemann London 1982 (7 November 1993)
Among a generally rigorous
book on ‘modern mathematics’, with chapters on Relations, Linear Programming,
Vectors and more way beyond me, surprisingly tessellation and also Escher-like
aspect finds an outlet. Tessellations, Chapter 10, pp. 194-205, and cover
tiling, unattributed, p. 200. This book has played a notable role in my early
studies, in which in 1987 I studied it extensively. However, the ‘Escher-like’
tessellations by Murphy show a complete lack of understanding of the issues and
are a veritable disaster!
Murphy, Patrick and Albert F. Kempf. The New Mathematics.
W. H. Allen London 1982 (18 October 1997)
Nath, R. History of Mughal Architecture (8 October 2018) PDF
The subject of recent October
2018 interest due to a stated 17e century Cairo tiling jali, in a
Simon Ray Indian and Islamic Arts catalogue. Nath appears to be the leading autoritet,
hence my interest in this four-volume set. This being so, I emailed him, asking
specifically about the Cairo tiling aspect, but he responded in a non-specific
Nasr, Seyyed Hossein. Islamic
Science: An Illustrated Study. World of Islam Festival Publishing Co 1976. (First saw Grimsby
library 16 November 1987, or at least the first recorded study, and studied
again later, c. 9-10, 12 August 1988, when photocopied pp. 88-90)
Studied as the book has a few
geometric aspects, although little on tiling, of which of most interest is pp.
76, 89-90, 147. Without the book to hand, downloaded as a PDF for the sake of bekvemmelighet (although the book is economically available). Nasr is a prolific
author, with 29 publications to his name (on the internet archive site), easily confused. However, my original book title reference is indeed as stated.
Much of the book had been
forgotten pending the download.
Nelson, David et al. Multicultural Mathematics. Teaching
mathematics from a global perspective. Oxford University Press 1993. (Newark
Buttermarket, 11 June 1994)
Chapter 6, Geometry and Art by
Julian Williams pp. 142-174 has a small feature on tessellation, but aside from
that chapter there is next to nothing here of direct interest.
note in the context of Escher cover art is a snippet of Escher’s plane tiling
de Swans on the cover (shared with
another, unrelated picture). Especially see Chapter 6, ‘Geometry and Art’, with a focus on tessellation, my field of interest. s. 158, of two (semiregular) tessellations, 6, 4, 3, 4 (Pavage de Diane) and 6, 12, 4 as line drawings, said to be from Shibam-Kawkaban, of a minaret in Yemen.
Nelson, David (editor). Dictionary of Mathematics.
Penguin Books, Second edition, 1998. First published 1989 (25 August 2007)
Serious reference guide. Tessellation
gets a brief mention, with two illustrations.
Newell, Peter S. Topsy
& Turvys. (2016)
Of note is the ambigram, p. 31
Newman, James A. ils
World of Mathematics – Volumes 1-4 Simon & Schuster
2480pp. (4 Volumes) (September 2016, pdf)
(Newman also wrote a foreword
à The Universal Encyclopedia of Mathematics)
Nicolas, Alain. Parcelles d’infini Promenade au jardin d’Escher.
(in French) Belin Pour La Science. 2006 (2010?)
Delightful! Nicolas is a
master of his craft. A must have for anyone interested in Escher-like
Nichols, T. B. and Norman Keep. Geometry of Construction.
Cleaver-Hume Press Ltd 1959. First published 1947. First saw 1987 (27 August
Of minor interest. Although of
a geometric construction premise, of first principles, at least to begin with, there
is indeed some patterns of interest. Fret patterns pp. 88-90, patterns based on
squares pp. 90-91, patterns based on circles, pp. 92-93 patterns in circles pp.
94-95 and tracery, pp.196-199. I believe I first saw this book in 1987, (at the
college library?) and loosely studied with some geometric constructions of the
day. There is no tiling as such.
Nisbet, Harry. Grammar of Textile Design. Scott, Greenwood & Son. First Edition 1906 276 pp. (seen). Second edition 1919, Third Edition 1927 (seen). (26 February, 8 March 2019) PDF
Of an undoubted expert on the subject. Has a Cairo tile unit block, ‘linear zigzag weave’, p. 101 (first edition), but I don’t at all understand the correlation between supposed related diagrams. That said, although doubts remain, surely a Cairo tiling is intended. This is of obvious note as one of the earliest examples, namely that of 1906.
Nixon, J. T. World of
Shapes. Oliver and Boyd Ltd. 1968 (5 October 1998)
Northrop, Eugene P. Riddles
in Mathematics. A Book of Paradoxes.The
English Universities Press Ltd. 1945 and also Penguin Books 1975. (16 November
1996 and 17 October 1998)
Largely popular account,
de ten chapters with the last of a more
advanced nature. Largely of paradoxes and fallacies, derived from stated
sources, as detailed in the preface. Not tessellation as such, but of much
related and other material of interest; of minor optical illusions, dissections,
space-filling curves, Mobius band, four-colour theorem to name but few. ils
overall tenure is largely of an advanced nature, although the above is indeed
of a popular level.
Nunn, G. Moderne
Mathematics. Macdonald And Evans. 1978 First saw c. 31 July 1987 (22
Small format paperback. qui
such, this book, first seen at the library, was studied very early, of 31 July
1987, of which my memory has unfortunately considerably dimmed; indeed, I
cannot now picture this, or indeed recall the study to any great extent. To aid
in reviewing the study, of which for the year of 1987 I am in the midst, I thus
ordered (it being reasonably priced), and not least given that it includes a
Cairo tiling. The book is typically of ‘modern mathematics’, of fifteen
chapters with favoured topics, such as Sets and Algebra, although of course
much of this is out of my realm of interest. Nonetheless, it contains dedicated
chapters on tessellations, pp. 155-163 and topology pp. 224-268, all of which I
had completely forgotten! As such, the chapter on tessellations is somewhat of
a let down. All very basic, although couched in technical terms. det er ingen
Escher-like element whatsoever. However, some most rudimentary Escher-like tessellations can be found on in the Appendix, p. 327, which is ‘typical
teacher’ i.e. not idea!
O’Beirne, T. H. Puzzles
& Paradoxes. Oxford University Press, 1965 (17 February 2015)
A collection of articles which
dukket opp i New Scientist de
January 1961 to February 1962. No tiling or Escher. Somewhat of a let down, in
that I was expecting some of his tilings columns to be shown.
Obermair, Gilbert. Matchstick Puzzles, Tricks & Games.
Sterling Publishing Co., Inc. 1978 Originally published in Germany under the
tittel Streichholz-Spielereien, Wilhem
Heyne Verlag, Munich 1975 (14 November 1998)
Small format hardback, 144 pp.,
14 Chapters. Popular tricks with matchsticks, with answers. Gives a history of
the match p. 7. P. 8 is interesting in that it shows how best to strike a match, in a counter intuitiv way,
not the more åpenbart lengthwise strike, but breadth! I had never even considered
this! To what extent the puzzles are original is not readily detectable;
certainly, there are no references or bibliography. Likely, they are a re-hash
of existing material, given the historical account below. Makes for a mildt amusing coffee-time reading, but there is nothing of significance here.
A brief history: From: Aims
Education Foundation on 12/3/2005 Source: http://www.aimsedu.org/Puzzle/3to5/index.html
In the 19th century matches
were first manufactured. Invented in 1827 by the British chemist John
Walker, matches soon replaced the tinderboxes that people had formerly used to
light fires. As matches grew in popularity and became ubiquitous
later in the 19th century, they spawned a new form of entertainment matchstick puzzles that became quite popular
when several match companies printed these puzzles on their boxes. Capitalizing
on this interest, publishers began to print books of match-stick puzzles. de
the turn of the 20th century, many people had developed a personal
repertoire of these puzzles and used them to challenge friends and
acquaintances. The toothpick puzzle presented here is modeled after these classical matchstick
Martin Gardner wrote about such puzzles in Scientific American November
1967 with the now famous "cherry in the cocktail glass"
O’Daffer, Phares.G; Clemens, Stanley R. Geometry. An Investigative
Approach 2nd edition Addison-Wesley Publishing Company 1992. (23
Chapter 4, 86-117 Patterns of
Polygons: tessellations, albeit very basic in scope. Has Cairo tiling page 95. Occasional usage of
Escher’s prints: Day and Night 86-88, Horseman 114, Magic Mirror, 215.
Ogawa, Tohru, Koryo Miura, and Takashi Masunari. Katachi U Symmetry. Tokyo:
Springer-Verlag 1996 (23 November 2016, Google book reference). Part 2, pp. 121-287 is available as a PDF
Especially see: William Huff.
‘The Landscape Handscroll and the Parquet Deformation’, 307-314. cette
has four new parquet deformations by ‘new people’, namely:
Alexander Gelenscer; Swizzle Stick Twirl, 1986
Pamela McCracken; Cloisonné, 1990
Loretta Fontaine; Seven of One Make Three, 1991
Bryce Bixby; They Come, They Go, 1991
Of interest: Analysis of Marcia P Sward Lobby Tiling by Teruhisa Sugimoto (Marjore Rice tiling)
Search of Convex Pentagonal Tiling with 5-valent NodesTeruhisa Sugimoto
Oguro, Sabu. Making
Marvelous Wooden Puzzles 70 Animal Families : 70 Animal Families
Fox Chapel Publishing, 2012 2014, 160pp. WANTED
Note that this is one of those books that although ostensibly in
print, are simply not disponible.
O’Keefe, Michael and Bruce G. Hyde. Crystal Structures 1. Patterns & Symmetry. Mineralogical Society of America, 1996, 453 pp NOT SEEN IN FULL
Of Cairo tiling interest, p. 207: The pattern is known as Cairo tiling, or MacMahon’s net et In Cairo (Egypt) the tiling is common for paved sidewalks…
The second use of the term ‘MacMahon’s Net’ for the Cairo tiling, having previously been used by them in their 1980 paper, ‘Plane Nets in Crystal Chemistry’, but this time in addition with the Cairo association. However, this is very much an ‘unofficial’ description. Upon correspondence with him (2012):
I suspect I got ‘Cairo tiling’ from Martin Gardner who wrote several articles on pentagon tilings. He is very reliable. As to ‘MacMahon's net’, I got the MacMahon reference from Cundy & Rollet….We are mainly interested in tilings on account of the nets (graphs) they carry.
Possibly, and plausibly, this by MacMahon, of 1921, was the earliest known representation, and so in a sense it was indeed broadly justified, even though by 1980 the ‘Cairo tiling’ term was coming into popular use, although if so, it is now been left behind by my subsequent researches. Curiously, the term is used on the Cairo pentagonal tiling Wikipedia page. However, the page leaves much to be desired, including this designation. Toshikazu Sunada has also used this term. However, I do not like this at all; it seems a somewhat artificial, additional naming, and seems unnecessary. Better would simply to have credited MacMahon as the first known instance (at the time) but without naming it after him.
Oliver, June. Polysymmetrics: The Art of Making
Geometrical Patterns. Tarquin Publications 1990. (6 April 1993)
Making very simple geometrical
patterns, of no real consequence, lightweight in the extreme, some with an
Islamic leaning due to her background in these designs.
Opie, Iona and Robert and Brian Alderson. The Treasure of Childhood. Books, Toys, and
Games from the Opie Collection. Pavilion Books Limited, 1989 (26 June 2016)
Oversize. Of minor interest as
regards puzzles and games, but full of interest in a general sense. Jigsaws,
with Spilsbury and others, pp. 152-153.
Opie, James (consultant author) with Duncan Chilcott and
Julia Harris. The Collector’s Guide to 20e
Century Toys. Bracken Books 1996 (first printed 1995) (26 June 2016)
O’Shea, Donal. ils
Poincaré Conjecture. In Search of the Shape of the Universe. Allen Lane, 2007.
(21 April 2012)
Osler, Dorothy. Machine
Patchwork Technique and Design. B T Batsford Ltd London First published
1980. First saw 16 June 1987
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed, led to minor studies of the day (1987),
as indeed with other patchwork books. However, now, and for some considerable
time, the nature of the material is considered hardly worthy the time
originally devoted to it.
No colour in book.
Ōuchi, Hajime. Japanese Optical and Geometrical Art. 746
Copyright-Free Designs for Artists and Craftsmen. Dover Publications Inc, New York 1977 (9 April
Flatters to deceive.
Essentially of ‘geometrical motifs’, as with Hornung. No tessellation as such,
save for one instance. No captions, index or discussions of the graphics
renders finding anything is much frustrating. Seemingly op art influenced. A
republication of the Japanese edition, titled Leading Part I. Of no real consequence.
Padamsee, Hasan S. Unifying
the Universe: The Physics of Heaven and Earth. IOP publishing Ltd, 2003 (Google
books, 16 June 2015)
P.132 Eight Heads.
Paling, D. Teaching
Mathematics in Primary Schools. Oxford
University Press 1982.
(15 October 2011)
Only of interest in a
historical sense, as it was one of the earliest* books on tessellation (and
maths per se) I studied, c. 1986. Tessellation pp. 272-272, with the ‘any
triangle, quadrilateral will tile’ rule. * Have I mixed this up with the book umiddelbart below?
Paling, D. and J. L. Fox. Elementary
Mathematics. Oxford University Press, 1965
From a reference in my own
early studies, of 26 January 1986, 1, 2 December 1986. Not sure if in
possession or not. The date here is not of the greatest clarity in terms of
certainty; 26 January may be misleading; in that with a 1 December listing, I
may simply have forgotten to change the year on the other.
Palmer, Kelvin. ils
Collector’s Guide To Cluster Puzzles Of The 1960s and 1970s. Self
Published. 2003. (5 November 2013)
Essential reading on the subject. History of
cluster puzzles (of the type as evinced by Escher’s Plane Tiling I et Plane
Tiling II as devised by Palmer’s father, Alex, of the 1960s, with
occasional reference to precursors of 1934 and 1943.
Pappas, Theoni. Mathematics Appreciation. Wide World
Publishing/Tetra Revised edition 1987. (3 June 1993).
————. The Joy of Mathematics. Discovering
Mathematics All Around You. Wide World Publishing/Tetra 1992. (3 June 1993)
Collection of popular
mathematics, typically over a two-page spread, sometimes three pages.
Tessellation pp. 120-122.
————. More Joy of Mathematics. Exploring
Mathematics All Around You. World Publishing/Tetra 1992 (3 June 1993)
Scandals. Wide World Publishing/Tetra. First published 1997, 3e
printing 1999 (31 August 2002)
A few good (brief) yarns,
although apparently no original research per se, with the material seemingly
taken from eksisterende sources in the bibliography. In short, essentially cuts to
the chase from other, more in-deth treatments.
Paraquin, Charles H. Eye Teasers. Optical Illusion
Puzzles. Granada Publishing Limited 1979 (19 July 1992).
Juvenile. Usual repeats of
Parsons, Richard. GCSE Mathematics Intermediate Level.
Coordination Group Publications 1998. (21 September 2004)
Pasztory, Esther. Pre-Columbian
art. Everyman Art Library. Weidenfeld and Nicolson, 1998 (22 October 2016)
A opportunistic purchase, from
a charity shop. Although not a maths book, included here as it discusses Escher-like
tessellations in broad terms, of which I recall Branko Grünbaum discussing like
aspects here. To be studied and assessed.
Paulos, John Allen. Beyond Numeracy. An Uncommon
Dictionary Of Mathematics. Penguin Books 1992 (30 April 1994)
————. Innumeracy. Mathematical Illiteracy and its
Consequences. Penguin Books 2000.
First published 1988. (no idea as to when obtained, at a guess, 2000-2005)
Popular account. Small format
paperback, of mild general interest, but nothing of note as regards my specific
Peak, David; Frame, Michael. Chaos under Control. The Art
and Science of Complexity. W. H Freeman and Company 1994 (3 August 2002)
Pearce, Peter and Pearce, Susan. Polyhedra Primer.
Dale Seymour Publications 1978 (24 October 1998)
Non attributed Cairo tilings on page 35,
and in the context of the Laves tilings, page 39.
Pearcy, J. F. F; Lewis, K. Experiments in Mathematics.
Stage 1, 2 and 3 (3 books). Longmans, green Co Ltd 1967. (17 August 1997)
Juvenile. A bit like
Mottershead, but for a younger age. Tessellations 14-15 (B1) reptiles 8-9 (B2).
Pedoe, D. The Gentle Art of Mathematics. Penguin
Books 1963. First published 1958 (18 April 1993)
Small format largely popular paperback,
160 pp. As such, although largely on popular subjects, there is very little of direkte interest to me here. Chapter 1
‘Mathematical Games’. Chapter 5, ‘Two-Way Stretch’, on topology, has elements
of interest. Chapter 6 ‘Rules of Play’,
is on symmetry, with a Islamic tiling p.
120. No other tiling.
From Wikipedia. Dan
Pedoe (29 October 1910, London – 27 October 1998, St Paul, Minnesota,
USA 1)) was an English-born mathematician and geometer with a career
spanning more than sixty years. In the course of his life he wrote
approximately fifty research and expository papers in geometry. He is also
the author of various core books on mathematics and geometry some of which have
remained in print for decades and been translated into several languages. ces
books include the three-volume Methods of Algebraic Geometry (which
he wrote in collaboration with W. V. D. Hodge), The Gentle Art of
Mathematics, Circles: A Mathematical View, Geometry and the Visual
Arts and most recently Japanese Temple Geometry Problems: San
Gaku (with Hidetoshi Fukagawa).
————. Geometry and The Liberal Arts. Penguin Books
1976 (14 July 2001)
Peitgen, Heinz-Otto et al. Fractals For The Classroom:
Strategic Activities Volume 1 Springer-Verlag 1991 (6 August 1997)
Volume 1 of a two-volume
series. As such, given their content I am at a loss to explain why I målrettet pursued these books (ordered from Claire Publications). Although I have a mild
interest in fractals, this is really only in passing, as the subject quickly
becomes highly technical, way beyond my understanding. I have a dim memory of
them being on offer, at half price, and so it seems that this was enough to
induce me. Whatever, the premise of the books are for the classroom, with the
six authors (Peitgen, Jürgens, Saupe, Maletsky, Perciante, Yunker) leading
lights in their field. Volume I (128 pp) is notably easier than volume 2 (187
pp). Even so, still much is obscure in the first. A graphics calculator seems a
prerequisite. Unsurprisingly, no tessellation or Escher. Simply stated, an
‘unwise’ purchase. I have no plans to re-read.
Peitgen, Heinz-Otto et al. Fractals For The Classroom:
Strategic Activities Volume 2 Springer-Verlag 1992 (6 August 1997)
As detailed above.
Penkith, F. E. Confidence Mathematics. Macmillan
Education Ltd. Reprinted 1990 (first edition 1985) (27 October 2001, Louth).
No tessellation. Parce que ~~ POS = TRUNC
mathematics, utilitarian, for 12-year-old. Of significance in that this was one
of the earliest maths book of all that I studied, c. 1986 or 1987.
Penrose, Roger. The Emperor’s New Mind. Concerning
Computers, Minds, and the Laws of Physics. Vintage Books 1989 (25 July
Mostly too advanced for me. Occasional
tessellation, of non-periodic tilings, and their background, pp. 172-178. Occasional
Escher references, Circle Limit I s.
203. Quasicrystals pp. 562-563.
————. Shadows of the
Mind. A Search for the Missing Science
of Consciousness. First published en
Great Britain by Oxford University Press, 1994. Vintage 1995. (5 November 2011)
Weighty tome, of 457 pp. As to be expected by the tenure of
the book, this is almost entirely beyond me, the only aspect that is vaguely understandable is a short
discussion on tiling in the context of the ‘tiling problem’, in Chapter 1,
‘Consciousness and computations’, with two pages of polyomino hit-parade, pp. 29-33, Robert Amman influenced. No Escher.
————. The Road to
Reality. A Complete Guide to the Laws of the Universe. Vintage Books London, 2004. Grimsby Library
Minor Escher references and
pictures, in conjunction with hyperbolic geometry, 33-35, 39 (all Circle Limit
I), 47 (Angels Devils, sphere, plane tiling). Advanced, to say the least!
Perelman, Yakov. Mathematics
Can Be Fun. Mir Publishers 1985
————. Recreativa Physics for Entertainment Figures for Fun, Fun with Maths &
Physics Arithmetic for entertainment, Mechanics for entertainment, Geometry for Entertainment, Astronomy for entertainment, Lively Mathematics, Physics Everywhere, Tricks and Amusements (1913)
Figures for Fun: Stories,
Puzzles and Conundrums. Gardneresque (10 May 2017, Internet book archive
download) Skim read. Minor geometric dissections 133, 140 and end.
Petersen, Ivars. The Mathematical Tourist. snapshots of
modern mathematics. W. H. Freeman and Company New York. 1988 (23 August 1994)
Chapter 7, pages 200-212, ‘The
Fivefold Way’, with Penrose tiles.
————. Islands of Truth: A Mathematical Mystery Cruise.
W. H. Freeman and Company New York.
1990 (30 April 1994).
See ‘Paving the Plane’, pp.
Petrie, Flinders W. M. Egyptian Decorative Art. Arno Press. 1978. First published 1895 (19 November 1994,
Checked for Cairo pentagon – no reference.
————. Decorative Patterns of the Ancient World.
Bracken Books. First Published 1930. Studio Editions Ltd 1995 (26 August 1995)
Checked for Cairo pentagon – no reference.
Phillips, Peter, and Gillian Bunce. Repeat Patterns: A Manual for Designers, Artists and Architects. Thames
& Hudson 1992.
First saw in art school
library, and duly studied, disproportionately so, the exact memories of which
have long since faded. The premise is of using a computer for drawing tessellations.
Pick, J. B. (Compiler). Dictionary
of Games. Aldine Paperbacks, J. M. Dent
& Sons Ltd., 1952
Subtitled as ‘Outdoor, Covered Court, Gynnsuim and Indoor’. Hvordan
to play 501 games
Of game and puzzle interest. Five
chapters, of (I) Full Dress, Outdoor Games, (II) Informal Outdoor Games, (III) Covered Court Games, (IV) Gymnasium Games, (V) Indoor Game, with many subchapters. Potted
details, rules and history of games, not illustrated. de most interest is (V) Indoor Games, with a
subchapter on Board and Table Games, pp. 229-263. However, there is nothing
overtly mathematical here. The background of Pick went unresolved.
Pickover, Clifford. (24 July 2016)
Pickover, Clifford. ils
Pattern Book: Fractals, Art, and Nature 1995. WANTED
Dewdney’s ‘informal tesselation
(sic) of Cats’ cluster puzzle picture. Not that he told me about this when we
Pieper, Jan and George Michell, editors. The Impuse to Adorn. Marg Publications
From a reference in Craig Kaplan’s thesis, p. 206. A reference to Haresh Lalvani and Pattern regeneration, on jalis.
Pinto, Edward & Eva R. Tunbridge and Scottish Woodware. G. Bell & Sons, 1970. c.
primarily of jigsaw history. Especially see plate 8, of a ‘treadle operated
jigsaw, by W. Fenner, about 1760’.
Pipes, Alan. Foundations
of Art and Design. Laurence King 2008. Grimsby Library.
Has occasional Escher, with Day and Night.
Pizzuto, J. J. and P. L. D'Alessandro. 101 Fabrics. Analyses and Textile Dictionary. New York: Textile Press, 1952 (8 April 2019). Viewed online at Hathitrust, seemingly not available as a PDF
From a reference in Grünbaum (Satins and Twills article). The premise is of a illustration of a term (cashmere etc) with a swatch, technical details and then dictionary entry at the end of the book. Popular account. Houndstooth p. 43 Glen Plaid p. 39. Note that no other terms I have studied are included, such as Shepherd’s Check, Border Tartan etc. Useful, convenient reference to the fabric terms in a generalised sense.
Plichta, Peter. God’s Secret Formula. Discovering the
riddle of the universe and the prime number code. Element 1997 (11
Pohl, Victoria. How to Enrich Geometry Using
String Designs. National Council of Teachers of Mathematics. 1986. Third
Printing 1991 (30 April 1994)
Geometric string designs, in
two and three dimensions. Ostensibly for children, 68 pp. No tessellation. qui
such, now, and for a considerable while, only of limited interest. For a while,
amid my geometric studies of 1987, I was interested in such designs, and so
likely with that in mind obtained the book by chance, from my visit to John
Bibby in York, where I had to make a choice of ‘buy or lose’ at the the time,
this of course predating the internet. Although of a popular geometric nature,
if seen for the first time I would now not be so enthused, and sikkert ikke på
cost price! Further, unlike other books from Bibby, this was not studied in any
way, and so this, even of 1994, reflects a realisation that this was not of direct
interest. Be that as it may, it just may have been, and so in that sense the
purchase was justifiable.
Polster, Burkard (with foreword by John Langdon). Eye
Twisters. Ambigrams & Other Visual Puzzles to Amaze and Entertain.
A prize in an Australian
tessellation contest that I won run by Polster. Very nice indeed, in the same spirit
as with John Langdon’s Wordplay.
Escher section: ‘Escher & Co, with Drawing Hands, Magic Mirror, Day and
Night, Relativity and other tessellations by Hop David, Ken Landry, Jos Leys, Peter
Raedschelders, Henry Segerman, William E. Wenger, and Alain Nicolas.
Pólya, G. How to Solve It. Doubleday Anchor Books.
1957 (Date not stated, 10+ years).
Of limited interest.
Price, Jeffrey. M. C.
Escher Amazing Images. (privately published book/catalogue). (28 March
Gift of Jeffrey Price. Much of
interest, with many previously unpublished materials and Price’s own insights
Priestly, J. B. Man and Time.
Aldus Books London
Pye, David. The Nature &
Aesthetics of Design. Barry and Jenkins Ltd 1978 (18 October 2008)
Pythagoras (the entire
archive). Mathematics journal in Dutch.
Non. 4, April 1998 (1 April 2016). A whole issue devoted to
Escher. Also of note is an article by Rinus Roelufs on the Cairo tiling ‘Tegels
Raba, Raoul. Zoo
Les Éditions Kangourou 1998 editor André Deledicq (In French) (14 March 2015)
Racinet, A. The Encyclopedia of Ornament. Studio
Editions 1989. Originally published as L’Ornement
Polychrome, 1856 and in English translation, Polychromatic Ornament
by Henry Sotheran and Co. London 1873). First saw Grimsby Central reference
library, 8 or 9 January 1989 (10 August 1993)
Essentially of ornament rather
than tessellations. Although of a tome of major undertaking, it is of little
direct interest as regards tessellation. Pages of interest, with tessellations,
include 77, 123, 129, 135 and 149, albeit there is nothing in the way of
innovation. Time constraints forbid an considered examination of the text. ils
two red and blue diagrams of Egyptian tilings, p. 77 are repeated in**. s. 129 and 135 are Arabic patterns.
that this book was studied briefly, almost derisorily, on 10 January 1989,
albeit seemingly of just a single sheet (amid non-related studies) and is of no
Fom Dover: Presents one
hundred plates in color, comprising upwards of two thousand specimens of the
various styles of ancient, oriental, and medieval art; inkludert
Renaissance and the seventeenth and eigtheenth centuries. Though he himself was
a distinguished painter and illustrator, Albert-Charles-August Racinet
(1825–1893) is best remembered for two monumental color-plate publications he
edited: Le Costume historique (Historic Costume) and L'Ornement
polychrome (Color Ornament).
L'Ornement polychrome, a visual record in color of ornament and decorative arts
from all over the world and throughout history to the end of the 18th century,
eventually included 220 plates. The first 100 plates (Series I) appeared in ten
installments between 1869 and 1873. A first edition of 5000 copies in volume
form was published shortly after the completion of the installments, a second
edition appearing as early as 1875.
This edition contains all the plates from Series I, with brief new English
captions that summarize the French text. The copious material, ranging from
Europe to Oceania and from ancient Egypt to just before 1800, is derived from
architecture, painting, woodwork, metalwork, leatherwork, textiles, and many
other art forms. Racinet's often-repeated purpose in publishing these
decorative masterpieces was the encouragement and improvement of the arts of
his own day, not only so-called fine arts but also the commercial arts involved
in the designing and selling of manufactured goods. Dover's reissue of the
plates, recognizing their perennial value and appeal, naturally is meant to
serve the same purpose. Racinet's breadth of insight and catholicity of taste,
truly enlightening for his day, give his selection a welcome variety and a
consistently high standard of excellence; while the consummate skill of his
artistic fellow workers and of his printer/publisher, the celebrated
Firmin-Didot company, make these plates true works of art in their own right.
Raeburn, Michael. un
Outline of World Architecture. First published 1973 Octopus Books Limited. (23
Although not a maths book per
se, included here nonetheless as it includes occasional tiling, and more
specifically a fused pentagon of a Cairo-like tiling at Amber Place, India, p. 55,
having not seen before.
Ranucci, E. R. and Teeters, J. L. Creating Escher-Type
Drawing. Creative Publications 1977. (15 October 1994)
Of its type, a good account of
generalen procédures of creating
Escher-like tessellations, although as neither Ranucci and Teeters (and Ranucci
in particular) can make any great claims as to talent in the field, the book is
held back somewhat. The all-important issues underlying life-like tessellation
are not discussed. Broadly, the book appears to be aiming at a juvenile
Ranucci, Ernest R. Tessellation and Dissection. J. Weston
Walsh. 1970 (The date stamp is only semi legible, apparently 2008 or 2009)
Somewhat of a lightweight
production, of just 79 pages. The mathematics is of a popular level, seemingly
of a school age nature, of about 12-14 years. Has a variation of the Cairo tiling, with two
pentagons, p. 36. As such, it has not influenced my studies directly.
Ravenna, Daniele. Australia
Puzzle: Contemporary Silverware & Jewellery. Photographs Mario
Tedeschi, text Daniele Ravenna. Sydney: Puzzle Pty, 1994. (November 2016)
Gift of Lorenzo Logi. Of note
is that it contains example of Angiolo Logi’s cluster puzzle work.
Rawson, Phillip. Creative Design A New Look at Design
Principles. Macdonald and Co (Publishers) Ltd 1987. (29 August 2005)
First came across the term
‘simulacrum’ page 150 from this book. Islamic pattern p. 90.
Rayner, D. Higher GCSE
Mathematics: Revision and Practice. Oxford University Press, 1994 (4 August
Textbook, and as such, of
limited interest; the book has no tessellation aspects per se, save for some ‘regular
pentagon loops’, albeit strictly of ‘patches’, p. 51.
Razzell, Arthur G. and K. G. O. Watts. Symmetry. Mathematical Topics 3. Rupert Hart-Davis 1967 (22 January
Read, Ronald C. Tangrams –
330 Puzzles. Dover Publications, Inc (18 March 2000)
Reader’s Digest Books and
Articles – see Moore, Alison, Keeton, Greg.
Rees, Martin. Just Six
Has Escher’s * and * pp**.
Reichelt, Gotz-Peter. Tier
welten (in German) c. 2003 (6 June 2016)
On his interlocking wood carved
animal puzzles, namely cluster puzzles. Most pleasing indeed, with quality
Renko, Hal; Edwards, Sam. Tantalizing Games for your
TI99/4A. Addison-Wesley Publishers Limited. 1983 (10 October 1993).
‘Early’ computer book, badly
dated. Purportedly ‘Escher’ pp. 50-54, with computer instructions, although
none of Escher’s tilings/prints are illustrated. So lightweight as regards
Escher to be barely worth the mention.
Rey, Marc Lachieze- and Jean-Pierr Luminet. Translated by
Joe Laredo. Celestial treasury. Form the
music of the spheres to the conquest of space. Cambridge University press,
2001 (15 August 2015)
Although on astronomy, has
sideways references to mathematics, namely with polyhedra, pp. 48-51, Jamnitzer
and Kepler p. 57.
Reyes, Encarnación and Inmaculada Fernández. Pentágonos. Construcciones. Mosaicos,
Geometría sagrada. (in Spanish) 2015. Universidad de Valladolid (21 January
Has much of interest in a
generalised sense, although hindered in understanding in that it is in Spanish.
P. 166 has an interesting ‘mixed’ Cairo tiling, with kites. A mention of myself and collaborator Helen Donnelly on pp.
74 and 156, and photos on the front
Reichmann, W. J. The Spell of Mathematics. Methuen
& Co Ltd First published 1967 (14 July 2001).
Small format hardback, 15
Chapters, 272 pp. Some popular
philosophical musings as to the attraction (or ‘spell’) of mathematics. de
limited interest. Too advanced in parts, but still largely accessible. aucun
tessellation or Escher. Perhaps of most interest is on the cycloid, pp. 160-161.
Also occasional geometry throughout the book.
Richardson, Margaret H. The Sign of the Motor Car. Dennis,
Massachusetts, 1926, privately printed. REFERENCE NOT SEEN
By a pioneeer of cluster puzzles. ‘A biographical sketch’, as
quoted by Anne Williams.
Riley, Noel. A History
of Decorative Tiles. Grange Books 1997 (11 June 2015, Grimsby library)
Examined on the likely
possibility of tessellation, but not so, at least of any substance.
Robertson, Bruce. Learn
to Draw Step-by-Step. Macdonald & Co (Publishers) Ltd 1987 (undated c.
Although not a mathematics
book by any stretch of the imagination, as it is primarily of art procedures,
as it contains Escher and pattern aspects, albeit briefly, I thus include. A
pastiche on Escher's Day and Night, p.
37. An interesting technique for drawing patterns is given, pp.178-179. cette
influenced my studies of the day when first seen, in December 1987.
Rogers, James T. The Story of Mathematics. Hodder and
(8 August 2004) History, 16-year-age range.
Rogers, Nigel. Consultant editor Dr Ian Gordan. Incredible Optical Illusions. A Spectacular
Journey Through The World Of The Impossible. Quarto, 1998. First published by in Great
Britain by Simon & Shuster Ltd. (28 April 2018)
Roojen Pepin van.
Islamic Designs From Egypt. Pepin Press, 2007 (7 August 2014)
Obtained on the off chance of
a Cairo tiling appearing, of whatever form. However, there is no Cairo tiling
in the book. Indeed, the whole book is one of relative disappointment, it
consisting solely of pictures, with each page of a tiling or pattern, but without
any text to put the pictures into context. Without such information, this thus
loses any overall value it may have had. On occasion, I recognise the picture
source (such as the ‘fused Cairo’), but this is indeed rarely.
The accompanying CD-Rom is of
a like nature.
Ross, Alistair. The story of Mathematics (as in
original). A & C Black (Publishers) Limited 1984 Fist saw in Cleethorpes
library c. 29 August 1987 (12 December 1998).
Rangoli and Islamic tilings p.
21. Use of Escher’s Relatively skrive ut
Frontispiece and p. 25. Juvenile. This led to studies of p. 21 (not
Escher-like), of three different periods, of August/October 1987, July 1988 and
January 1991. As such, the studies were of relative depth of the day, albeit
now, and for some time, somewhat overstated as to their inherent importance.
T. Geometrical Exercises in Paper Folding.
Madras, 1893. Edited and Revised by W. W. Beman and D. E. Smith, Chicago 1917 (Downloaded
from Internet 13 May 2015)
From a reference in MacMahon, although noted before andre steder. Begins
with a few simply polygon folds, before moving on to more advanced work. A book
full of interest, although whether I will be able to find the time to study this
is any degree of depth (or indeed in passing) is doubtful. Has a small section (five
pages) on pentagon folding, but not relevant to tiling matters.
Rowland, Kurt. Looking and Seeing. Notes for
teachers. Book 1 Pattern and Shapes. Book 2 The Development of Shape.
Book 3 The Shapes We Need. Ginn and Company Ltd. 1965 (2 July 1995)
All books are text only.
Roza, Greg. An Optical
Artist: Exploring Patterns and
Symmetry. The Rosen Publishing Group, Inc. 2005 (28 March 2011)
Gift of Jeffrey Price. Has
Escher cover of Hand with Reflecting
Rubin, Don. What’s the
Big Idea? And 35 other unusual
puslespill. J.B. Lippincott Company 1979. (9 July 1995)
Rucker, Rudy. The Fourth
Dimension: A Guided Tour of the Higher Universes. Houghton Mifflin, 1984. A later edition is of 2012, with
a change of subtitle (30 December 1989) NOT IN POSSESSION
A popular account of advanced
concepts. A minor study worked on on 2 January 1990, first seen at Grimsby central
library, long since deleted from stock. Nothing on tessellation per se in my
The book is available for free
on his website (and with other publications of his, notably Infinity of the Mind), but without the
page numbers, which means finding references is a chore. Minor Escher reference
with pseudsosphere p. 108.
Russell, Betrand. Wisdom
of the West. First published by MacDonald & Co (Publishes) Ltd, 1959.
(28 May 2005)
On philosophy, with occasional
mathematical references. However, finding and sorting ‘useful’ maths here for
my purposes is few and far between.
T. M. Mathematical Pattern. Mathematics for the Majority. Chatto &
Windus 1971 (22 August 2004).
One book of the seven-part
‘Mathematics for the Majority’, series, of which I have two. The book seems to
have been compiled by a ‘project team’, with one primary author stated. ils
books are stated as ‘Chatto & Windus for the Schools Council’, which thus
gives the intended audience. The back cover states ‘This Schools Council
project was set up to further the teaching of mathematics in secondary schools
to children of average and less-than-average ability’. Also see Machines, Mechanism et Mathematics by A. E. Bolt and J. E.
Hiscocks for another I have in this series.
‘pattern’ in the broader sense, of number and geometry. The topics of this book
are broadly out of my mainstream interest, but it still has isolated aspects of
interest. There is no tessellation. Symmetry pp. 25-28, Polyhedra pp. 36-37,
Golden Section pp. 61-63. Has interessant book list, pp. 66, with unknown E J.
James reference and series of ‘Topics of
Sabin, Francene and Louis. ‘The One, The Only, The Original Jigsaw Puzzle Book’. Chicago Henry
Regnery Company, 1977 (11 April 2017)
From a reference in Williams,
although found first by ‘favoured chance’ on the web, of the first chapter, An Irreverent History of the Jigsaw Puzzle qui
‘showed promise’, hence a speculative purchase. A somewhat quirky book,
seemingly primarily of a humorous premise rather than any attempt at scholarly
insight. Overall, rather silly, with alternate chapters of a single page….
Although there is indeed a history, in which Spilsbury’s place is detailed, the
impression given is that this is the authors own research, as no references are
given. However, this is not so; without doubt, the Sabins are borrowing from
Hannas. You win some and you lose some…
Sackett, Dudley. The Discipline of Number. Foundations of
Mathematics. Sampson Low, Marston and Co: London 1966. (Junior) (24 October 1996 or
Sackson, Sid. A Gamut of Games. Hutchinson & Co.
Ltd. 1983. First published 1969 (27 August 1997)
Gardneresque. Stated on the
back cover as ‘diversified collection of 38 remarkable, intellectually
stimulating indoor games…. many of the book’s best games are the invention of
the author’. Martin Gardner praises it. In six sections. Each section begings
with a small essay, followed by the games. Has a useful section on ‘short
reviews of ganes in print’, pp. 188-221. Sackson is widely recognised as an
authority on games, and game history.
general interest, but much of the material, being non-geometrical, is of little
direct interest. C'est ideal for
reference purposes, but not for actual study.
Salvadori, Mario. ils
Art of Construction Projects and Principles for Beginning Engineers & Architects
(25 October 2014) Chicago Review Press 1990, third edition
Occasional crossover to
Sanchez, Miguel. The Alhambra and the Generalife. Publisher
unclear. 1976. (5 December 1992, small and 30 August 1998, large)
No Cairo pentagon.
Sarcone, Gianni A. and Marie-Jo Waeber. Amazing Visual Illusions. Arcturus Publishing Limited, 2011 (5
Although not a maths book it
is included here as it has crossovers. Popular account. Yoshifugi Utagawa (not
credited) cover and p. 27, with elephants and children; Duck/Rabbit p. 58 in
Fliegende Blatter, 1892, Escher’s Relativity,
s. 74. Convex and Concave, p. 74. Occasional new illusions.
Sardar, Ziauddin, and Iwona Abrams. Ed. Richard Appignanesi.
Introducing Chaos. Icon Books UK
2002. (date unclear, 2002?)
Popular account of chaos, as a
part of a series of like books.
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 1998 (7 March 2006) South
Western College, Kansas.
(The first Proceedings)
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 1999 (7 March 2006) South
Western College, Kansas.
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 2000 (7 March 2006) South
Western College, Kansas
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 2001 (7 March 2006) South
Western College, Kansas
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 2002 (7 March 2006) Towson University (Fifth)
Sarhangi, Reza; Carlo Séquin (Ed). Bridges. matematisk
Connections in Art, Music, and Science. Conference Proceedings 2004 (7
March 2006). South Western College,
Sarhangi, Reza; Moody, Robert V. (Ed). Renaissance Banff. Bridges.
Mathematical Connections in Art, Music, and Science. Conference Proceedings
2005 (7 March 2006). Canada
Sarhangi, Reza; John Sharp (Eds). Bridges. matematisk
Connections in Art, Music and Science. Conference Proceedings 2006 Tarquin
(10 August 2006) London, England (Ninth)
Sarhangi, Reza (Ed). Bridges. Mathematical Connections in
Art, Music, and Science. Conference Proceedings 2008 (7 March 2006) Towson University
Leeuwarden, Netherlands (Tenth)
Cairo reference and diagram page 102. B. G. Thomas and M. A.
Hann in ‘Patterning by Projection: Tiling the Dodecahedron and other Solids’
gives an equilateral pentagon
There are, however,
equilateral convex pentagons that do tessellate the plane, such as the well
tessellation shown in Figure 1. Also, other minor references essentially in
Bridges & Passages. Outdoor Exhibitions. Bridges 2008 Leeuwarden Catalogue
Collection of essays of
featured artists in churches: Istvan Orosz, Yvonne Kracht, Ulrich Mikloweit,
Koos Verhoeff, Rinus Roelufs, Oscar Reutersvärd, Gerard Caris, Elvira Wersche.
Occasional use of Cairo tiling by Roelufs,
but not credited.
Sarton, George. The Study of the History of Mathematics
& The Study of the History of Science.
Two volmes bound as one. Dover Publications Inc. New York 1954 (7 December
Free, college library. A
serious, though still readable
discourse. I find the book a little odd. It is essentially a study of a
study! I can’t see how I could gain from
Sattin, Anthony and Sylvie Franquet. Explorer Egypt.
AA Publishing. Reprinted 2000. First published 1996 (not seen). (18 May
Although not a maths book in
any way, included as it has incidental instances of the Cairo tiling. Typical tourist guidebook, picture
heavy. Two sightings, page 47, of the Old Cataract hotel, and page 222, of the
relics in the Al-Alamein war museum grounds. Both pictures are not ideal, with
as usual the subject matter being not the pavings themselves. Of the two, the
Cataract instance is by far the best, but even so, one requires foreknowledge
to discern individual pentagons, albeit it is not too far from being
identifiable as distinct pentagons. The Al-Alamein sighting is much the poorer,
taken at a raking angle, and only with foreknowledge is the tiling known, the
picture is essentially of square tiles in a chequerboard formation.
Sautoy, Marcos du. Finding
Moonshine. A Mathematician’s Journey Through Symmetry. Fourth Estate, London. 2008. Library.
Many occasional references to
Escher, mostly in passing. Those of note include pp. 24-26, 76-79.
————. Symmetry. A
journey into the Patterns of Nature. Harper Perennial 2009. First published
in Great Britain as Finding Moonshine.
(3 January 2015)
Much of general interest, of
12 chapters built around the year, but especially of October: The Palace of
Symmetry 62-87, with Escher heavily featured, Alhambra tiling discussion. un
old fashioned ‘good yarn’, with complex mathematics discussed in simplified
terms for the layman. Nice discussion on Simon Norton among others.
Sawyer, W. W. Prelude to Mathematics. Penguin Books
1961. (9 July 1994).
Small format paperback, albeit
of 214 pages. Of limited interest, due to the nature of Sawyer’s writings,
which largely focus on calculation, not my forte. although there are chapters
ostensibly of interest, such as Chapter 6, ‘Geometries other than Euclid’s’,
and Chapter 12, ‘On Transformations’, these are still advanced for me. As such, I find Sawyer’s writings (like Coxeter’s), not
conducive to my understanding (my fault, not theirs). I am not inclined
to re-read this.
From Wikipedia: Walter Warwick
Sawyer was born in St. Ives, Hunts, England on April 5, 1911. He
attended Highgate School in London. He was an undergraduate
at St. John's College, Cambridge, obtaining a BA in 1933 and
specializing in quantum theory and relativity. He was an
assistant lecturer in mathematics from 1933 to 1937 at University College,
Dundee and from 1937 to 1944 at University of Manchester. From 1945
to 1947, he was the head of mathematics at Leicester College of Technology.
In 1948 Sawyer became the
first head of the mathematics department of what is now the University of
Ghana. From 1951 to 1956, he was at Canterbury College (now the University
of Canterbury in New Zealand). He left Canterbury College to become
an associate professor at the University of Illinois, where he worked from
winter 1957 through June 1958. While there, he criticized the New
Math movement, which included the people who had hired him. From 1958 to
1965, he was a professor of mathematics at Wesleyan University, where he
edited Mathematics Student Journal. In the fall of 1965 he became a
professor at the University of Toronto, appointed to both the College of
Education and the Department of Mathematics. He retired in 1976.
Sawyer was the author of some
11 books. He is probably best known for his semi-popular works Mathematician's
Delight and Prelude to Mathematics. Both of these have been
translated into many languages. Mathematician's Delight was still in
print 65 years after it was written. Some
mathematicians have credited these books with helping to inspire their choice
of a career.
Sawyer died on February 15,
2008, at the age of 96. He is survived by a daughter.
————. Vision in Elementary Mathematics. Introducing
Mathematics: 1. Penguin Books 1964 (2 April 1994)
Small format paperback, albeit
of 346 pages.Of limited interest, due to the nature of Sawyer’s writings, which
largely focus on calculation, not my forte. The first in the series of four books (of which I have two) on the
pemise of ‘Introducing Mathematics’. Better than his other book ils
Search for Pattern. However, I
find Sawyer’s writings (like Coxeter’s), not conducive to my understanding (my
fault, not his) I am not inclined to re-read this.
————. The Search for Pattern. Introducing
Mathematics: 3 Penguin Books 1970. (17 September 1994).
Written in the same vein as
with the first book in the series, as detailed above, and of which the same
Not recreational maths.
Sawyer, W. W (ed.) Mathematics in Theory and Practice.
Odhams Press Ltd. 1948 (29 November 1992)
Very much of its day, with
much calculation, although that said, much is readable.
Scharf, Aaron and Stephen Bayley. Introduction to Art. The Open University. An Arts Foundation
Course, Units 16, 17 and 18 (30 March 1994, Boston)
Escher’s Circle Limit IV, pp. 172-173, discussed in the context of dual
function of shape.
Schattschneider, Doris. Visions of Symmetry. Notebooks,
Periodic Drawings, and Related Work of M. C. Escher. New York. W. H. Freeman and Company 1990. (20
Revised edition 2004 (23 March 2010)
Indispensable! Highligh after
Schattschneider, Doris and Wallace Walker. M.C. Escher
Kaleidocycles. Tarquin Publications 1982 (19 August 1988)
Cairo like tiling, p. 26, and
a short discussion as to Escher’s. I also have a German edition, M. C. Escher Kaleidozyklen.
Taschen 1992 (10 August 1993).
Schattschneider, D. and M. Emmer (editors). M. C.
Escher’s Legacy. A Centennial Celebration. Springer. First edition 2003,
paperback 2005. Springer (31 August 2005)
41 papers from the conference,
full of interest. Highlights include Rice’s, ‘Escher-like patterns from Pentagonal
Tiles’, pp. 244-251. Brief von Hippel reference p. 60.
Schlossberg, Edwin; Brockman, John. The Pocket Calculator Game Book 2. Corgi Books 1978 (18 October
Hermann. Mathematische Mussestunden. Volumes
I, II and III. Leipzig 1898.
(Downloaded from internet 14 May 2015)
From a reference in MacMahon. In three volumes. Volum
I has nothing in the way of tilings or polyhedra. Chapter on 1-15 puzzle, 133
(142). Volume II. Again no tilings or polyhedra. Has a chapter on Geometrical
Problems pp. 112-126 (129-138), but without tilings. Volume III appears of a more technical nature, mostly text,
of few diagrams. Nothing on tilings and polyhedra.
————. The Fantastic World of Optical Illusions.
Carlton Books 2002 (date has faded, 2007)
Although not strictly a
mathematics book it is included here nonetheless, as it has a loose crossover.
Delightful. Mattheau Haemakers dressed as man holding an impossible cube. s.
14, Escher portrait tiling by Ken Landry on frontispiece and p. 272, a physical
model of Escher’s Belvedere, p. 273. Penrose stairs p. 290.
Scripture, Nicholas E. 50
Mathematical Puzzles and Oddities. Van Nostrand 1963 Viewed (not
downloaded) at Internet Archive, 1 March 2018
Small format, 83 pages. Stated
as for teachers to enliven lessons. Covers a broad mathematical puzzle
spectrum: Oddments in Artithmetic, Oddments in Algebra, Oddments in Geometry,
Miscellaneous Oddments, Answers, Book List (although the book list is not
seen!). By far the most interesting is on Oddments in Geometry, although there
does not appear to be anything too original here. Discusses Geometric
Dissections, pp. 52-54, including Perigal’s dissection pp. 52-53. Although most
is popular, it has all been seen before. No tessellation.
The author, largely
unknown, appears to be of a
puzzler/mathematician, as he has (at least) two other like books to his name.
————. Puzzles and Teasers. Faber and Faber. First
published 1970 (24 October 1998)
Small format hardbook, 96
pages. Dudeneyesque. Covers a broad puzzle spectrum: Mathematical Puzzles, Logic Puzzles, Crossword Puzzles, Word
Puzzles, Vocabulary, Literature and General Knowledge, Oddity-Box, with
solutions. Nothing geometrical. To what, if any extent these are original is
not made clear.
Sealey, L.G. W. The Shape of Things. Basil Blackwell Oxford 1967 (12 October
Juvenile 10-years-old audience.
Seckel, Al. Incredible Visual
Illusions. Arcturus Publishing Ltd, 2005 (not stated) (guess 2008?)
Wide ranging. Yohifugi Utagawa
Ten Bodies and Five Heads p. 158, titled as a ‘change in meaning illusion’ (not
credited) C. 2005 Escher ‘section’ pp. 117-119, with Belvedere, Waterfall and
Ascending and Descending. Fish Tesselation p.50 (unaccredited (stated as),
Original face/vase illusion p. 48 ‘American Puzzle cards’ by E. K Dunbar and Co.
Seiter, Charles. Everyday
Math for Dummies. Hungary Minds Inc. 1995 (17 April 2005)
Seitz, William C. ils
Responsive Eye. The Museum of Modern Art, New York, in collaboration
with the City Art Museum of St. Louis, and others, 1965. (23 December 2016) PDF
Eye catalog commemorates the show of the same name at the MoMA in 1965. A
show several years in the making, it was the first to introduce the public to
Optical (or ‘Op) art.
Artists featured in the show
and catalog include the well-known Victor Vasarely and Joseph
Albers as well as the sensational and underappreciated Paul
Feeley and collective work by Equipo 57, a group of Spanish artists,
Of note is painted
tessellation by Equipo 57 (a Spanish collective), p. 23; Schröeder’s staircase
s. 31; and Mavignier p. 33, of whom has a loose parquet deformations of sorts
and of which upon subsequent searching has other works a like nature.
Serra, Michael. Discovering
Geometry. Key Curriculum Press, 2008 (30 August 2016, select part seen
Note that I have only seen a
small part of the book, namely Chapter 7, made available on the web, namely
transformations and Tessellations. Of most interest is chapters 7.4-7.7. ils
book is aimed at a school age audience, of 11-16. Of perhaps most note is that
of P*, where I discovered Rice’s connection of the Type 13 pentagon, derived
from a Cairo tiling. the conjunction of the tiling, and the Cairo tile, put the
seed in my mind, although this is not made clear in the book. Also of interest
are some children’s tessellations. Although these are mostly typical, of poor
understanding, a few are markedly better than others, such as ‘Perian Warriors’
by Robert Bell and ‘Sightings’ (Elvis Presley) by Peter Chua and Monica Grant
henholdsvis. Use is made of Escher's prints. As such, there is nothing new
here, aside from the original artwork, but nonetheless a welcome basic
introduction to tessellation and Escher-like aspects.
Seton-Williams, Veronica and Peter Stocks. Egypt. Blue Guide. A & C Black
Publishers Ltd Second Edition 1988
Obtained, by a chance finding,
of possible Cairo tiling interest. Described as a description and travel guide,
and furthermore of an scholarly (although still readable), extensive nature, of
a narrow fomat paperback, of 743 pages! Simply stated, this was seen at a car
boot sale, and of which it was thus impractical to view for Cairo tiling aspects.
On the off chance of usefuness, duly obtained. Upon a more leisurely read,
there was no Cairo tile references in any capapacity. But there might have
been! The matter is at least settled, rather than regretting having left the
possibility open-ended. Previously, the term Blue Guide (from the colour of the
cover) was unknown to me. From Wikipedia:
The Blue Guides are a series of highly detailed
and authoritative travel guidebooks focused
on art, architecture, and (where
relevant) archaeology along with the history and context necessary to
understand them. A modicum of practical travel information, with recommended
restaurants and hotels, is also generally included.
Seymour, D; Britton, J. Introduction to Tessellations.
Dale Seymour Publications 1989 (8 March 1995)
Cairo tiling, but not attributed, p. 39.
Seymour, Dale. Introduction to Line Designs. vallée
Seymour Publications 1992 (10 August 2006)
————. Geometric Design.
Dale Seymour Publications 1988 (24 October 1998)
Various geometric designs,
based upon circles, as in the style of Hornung. The book is pitched at a late
junior school age level, and is picture led, with simple geometric
constructions given, and then latterly, in the appendix, such as a bisecting a
line; the only text is the appendices. There is no tiling as such. As such, the
book has not influenced my studies in any way.
Sharp, Richard; John Piggott (ed.) The Book of Games.
Artus Publishing Company. Date faded 2000?
Card and board games.
Shaw, Sheilah. Kaleidometrics: The art of making
beautiful patterns from circles. Tarquin Publications 1981 (3 June 1993)
Broadly, a ‘geometric design’
book per se. This concerns making symmetrical designs of a ‘Kaleidoscope’ theme
using circles as the underlying framework, with 22 examples, and with text,
likely purposefully, at a minimum. It is not clear as to the target audience.
No mathematics at all really. The book lacks structure; it has no formal
contents and introduction. As such, there is very little of direct interest for
me here, save for page 23, which has a ‘whirling squares’ tessellation. ils
designs are somewhat repetitive and trite; a multitude of such examples are
possible. No tessellation as such. The book is lightweight, of just 40 pages.
Shefrin, Jill. Neatly
Dissected, for the Instruction of Young Ladies & Gentlemen in the Knowledge
of Geography: John Spilsbury & Early Dissected Puzzles Cotsen Press,
1999 (6 December 2016)
Speculative purchase on
account of the book being frequently quoted in serous jigsaw bibliographies.
Some outstanding research of the highest order on Spilsbury by Shefrin. en
particular, each of the five puzzles in the cabinet are examined and described
in depth. Although a slim volume, of just 40 pages, the content is most
interesting. One shortcoming is that it lacks an index. Darton mention on p.
————. Such Constant
Affectionate Care: Lady Charlotte Finch, Royal Governess & the Children of
George II. Cotsen Occasional Press, 2003 (3 June 2017)
Some outstanding scholarship
by Shefrin. Has much new insight on Mme Beaumont pp. 69-76 (and elsewhere) and
Spilsbury, and with a inventory of his known dissected maps. Also the much discussed
cabinet, with attached note as to provenance and claim. And of course on Finch
herself. Will stand numerous re-readings. Also of note is a possible precursor
to the four-colour problem, p. 8
————. The Dartons – A
Bibliographic Checklist. Hes & de Graaf 2009 WANTED £125
Shubnikov A. V. and N. V Belov. Coloured Symmetry. Pergamon
Press 1964 (13 October 2006)
Largely academic, and so
mostly beyond me; mostly concerning group theory and crystallography elements.
Very occasional tessellation – see ‘Mosaics for the Dichromatic Plane Groups’,
s. 220, with a pull-out. However, even this is theoretical. One aspect of
interest here is diagram 10, which resembles the famous Café wall illusion, but
with parallelograms, rather than rectangles. Also see Plate 1, on p. 229 for
further tiling diagrams, but of such simplicity of no real interest.
This also contains obscure
crystallography articles by Russian authors, such as Belov, as an English
Shubnikov, A. and V. Koptsik. Symmetry in Science and Art.
Plenum Press 1974 (12 December 2006)
Symmetry in all aspects.
Somewhat difficult to assess. Largely of an academic nature, but with
occasional aspects of a recreational level. Cairo tiling p 180, albeit by default of
quadrilateral tilings p. 176-179. Escher lizards, unicorns figures pp. 228-229
(colour plate), birds p. 364, winged lions p. 365.
Interestingly, as regards to
the winged lions’, Schattschneider (1990) also refers to this as a ‘winged
lion’, despite these creatures bearing little resemblance to a lion, wings or
not. Was her description taken/influenced by Shubnikov? She knew of this book.
Sibbald, Tim M. and Miranda
Wheatstone.. ‘Advancing Escher art through generalization’. Ontario Association for Mathematics
Education Gazette, 54(4), 23–26, 2016. (9 February 2018)
Escher aspect is somewhat overstated.
Singh, Simon. Fermat’s Last
Theorem. Fourth Estate, London
1998 (19 February 2007)
————. The Code Book. Fourth Estate, London
1999 (30 June 2013)
Singmaster, David. Notes on Rubik’s ‘Magic Cube’. Self
Published, Fifth Edition, 1980. (20
format paperback 68 pp, of condensed text. One of the earliest books on the
Rubik cube, at the height of the craze. Written from a group theory viewpoint,
with much of the text way beyond my understanding. Likely, I quickly gave up on
this! Mentions a few high profile names who I didn’t know were interested in
this, such as Roger Penrose and PeterMcMullen.
Silverman, David L. Your Move.
Kaye & Ward. 1971 (24 October 1998)
100 various puzzles and games
under various descriptions, all at a popular level, such as ‘Potpurri I’,
‘Bridge’, ‘Chess and Variations’, ‘Checkers and Variations’ etc., with each
puzzle on a single page followed by the answer. No tiling or polyhedra.
Sirett, Natalie. Drawing Visual Illusions. How to Have Fun Creating Masterpices of
Deception. Arcturus Publishing,
First saw I believe 2010, Grimsby Library. (20 May 2017)
Popular account, 128 pp., of visual illusions,
with Escher’s Relativity on the cover.
A veritable disaster, from start to finish; the author has no grasp of the
subject whatsoever! Where to begin? Shortcomings and incorrectness abound. ils
book is loosly themed upon six sections titled as ‘games’. Escher and
tessellation is to the fore, with many references. Section 3, Games with
Pattern, pp. 56-83 contain tessellations, of both ‘Escher-like’, as devised by
the author, and ‘pure’ tilings, such as the semi regular. The premise is one of
a tutorial nature, with guidance of how to create Escher-like motifs. Quite
frankly, this section has to be seen to be believed! The tessellations shown
are typical of people with no understanding of the subject. Just four
tessellations are shown, supposedly of an octopus, two different birds (one in conjunction
with a star), and a starfish. I cringe at these. All of these are particularly
bad. No, that’s too generous, instead read quite appalling, of no artistic
merit whatsoever, all undeserving of being in a book. Not a single tessellation here is of any worth. The standard is quite
appalling. What can one say of this quite sorry mess? This is unforgivable. Aside
from Escher and tessellation, a series of other illusions are supposedly
discussed, but the treatment is so slack. Even aside from the content there are
errors in the text and incorrect statements:
P. 18. Cube
illusion of ‘three ways’
P. 40. Narcisus starving to death
P. * absolulutely unique’.
P. 69. It is stating that Escher’s
periodic drawing 110 is undated. Really? This is news to me. This can be seen
on the drawing itself as 1961 – see Visions of Symmetry. A case of simple lack of checking, of which Sirett couldn’t even be
bothered to spend a few seconds finding out. And I suspect many others, of
which I lack the will to confirm.
Further, her artwork is no nore than that an average school child. Amazingly
she was ‘trained in Fine Art at the University of Newcastle-upon-Tyne. Studied
painting and drawing at the Royal Academy Schools, London’.
lacks a bibliography.
Finally, Sirett is completely unknown in tessellation circles. How she can have
the audacity to pronounce herself as an authority on the subject with these
truly sorry examples is unbelievable.
Slade, Richard. Geometrical Patterns. Faber and Faber
Limited, 1970. (24 October 1998)
The jacket describes as ‘This
is a fascinating book for children….’, which gives the intended audience. Slade
describes himself as a teacher of handicrafts. He is also the author of nine
other books on handicrafts, with possible interest Patterns in Space although from the jacket description inclined
towards the handicraft aspect. Many photos are from the British Museum and
Victoria & Albert Museum. The term patterns is used in a broad sense, with
lines, polyhedra, divisions of squares, circles etc. The book is not just on patterns per se, but
includes basic drawing tools and hints
and definitions. Of most interest as regards tilings is pp. 66, 69, describes
as ‘networks’, and ‘some types of pattern’ containing a variety of simple tilings. However, there is nothing
here that has not been seen before, as to be expected, given the intended
audence. Reference to counterchange p. 68.
Has an interesting historical French
curve source reference, page 16, crediting this to a ‘Professor French, a
mathematician’ different from others. Islamic design on front cover, and
repeated p. 37. Eight chapters, with Chapter 6, the most indepth, and of most interest.
Slocum, Jerry, and Jack Botermans. Puzzles Old & New:
How to Make and Solve Them. 1999 third edition. (10 August 2006)
Mostly of manipulative
puzzles, with historical details, all of a popular level. Delightful. Upon a
re-reading of 6 June 2014, I happened to notice a cluster-type premise puzzle,
s. 40, of animals based on the set of 12 Pentominoes in a rectangle, as
designed by the Japanese teacher Sabu Oguro, and produced commercially by
U-Plan, Japan! Somehow, in previous re-readings, I must have seen this and
overlooked its significance. Indeed, I do recall that I was entirely been
dismissive of it! Only with the foreknowledge of the cluster puzzle can it now
be appreciated. As such, I have seen this puzzle elsewhere in recent times, but
without background detail as given by the authors; this I can now follow-up.
Sam Loyd Trick mules and true
source p. 34. No jigsaw puzzles as such. Good bibliography.
————. The Book of
Ingenious and Diabolical Puzzles. Three Rivers Press; 1st edition November
1999 (7 March 2017)
Popular puzzle book. Primarily
purchased in regards of my cluster puzzle investigations, in that it recently
came to my attention that one of the puzzles mentioned ‘The Jayne Fishing
Puzzle’ p. 15, has possible relations, and so thus purchased, although of
course with the bonus that the book per se would be of likely interest.
However, in this instance, this was merely of a general packing nature, rather
than of a higher standard of double contours. But it could have been…. Has much
of a general interest without being of an overarching concern. Has eight
chapters of various puzzle classification. Of note is Mayblox of MacMahon, pp.
34-35. Much is indeed new, and can be read again with profit.
Sly, A. J. GCE O-level Passbook Modern Mathematics.
1976 (20 September 1992) Textbook
Victoria; Smeltzer, Patricia. Mathematics
Encyclopedia. Burke Books 1980 (18 February 2000?)
Juvenile, 10-year-old. Tessellation
page 75. Hexagons, not worth mentioning.
Smith, Cyril Stanley. A
Seach for Structure. The MIT Press, 1983. WANTED
Has Cairo tiling diagram,
without attribution, found indirectly in a excerpt page in the Indian journal
‘Resonance’, of June 2006.
Smith, Thyra. The Story of Measurement. Basil
1968. (12 October 2002).
————. The Story of Numbers. Basil Blackwell Oxford. 1969. (12 October
Smith, Charles N. Student
Handbook of Color. Reinhold Publishing Corporation New York, 1965. (24
January 2015) First saw at least 5 January 1987, College library
Although not a maths book per
se, it is included nonetheless as it was studied with my early maths studies of
1987, it containing a few geometric tilings, such as p. 57, as well as optical
Smith, David T. Miscellaneous Musings. Published by J. W.
Northend Ltd, West Street, 1929, and 1936. Illustrations by Elspeth
Eagle-Clarke (24 November, 6 December 2016).
Upon my interest in Elspeth
Eagle-Clarke’s work in cluster puzzles, I investigated her further, of which I
found a book reference, with illustrations by her, of Miscellaneous Musings. Therefore, I thus decided to investigate
this reference, albeit with the likelihood of nothing cluster puzzle related,
albeit with the possibility of background details of her. As I presumed Elspeth
Eagle-Clarke illustrations/references would be in the 1929 first edition but
not there! Continuing, I then obtained the 1936 edition where this reference was
indeed stated. as such, in relative terms it was a disappointment. save for the
credit, no other mention is made of Eagle-Clarke. There are 14 illustrations,
in black and white, on pp. 5, 9, 16, 27, 45, 46, 52, 65, 73, 79, 85, 111, 117
and 119. The artwork is nothing special per se, a mixture of straightforward scenes
from life and occasional fantasy aspects. Many references in the book allude to
Eagle-Clarke’s cluster puzzle work, with Pterodactyl and her Yorkshire
background. An intriguing possibility is that she was married to Smith. cette
idea was put in my head by a reference to the book, where she was so titled, of
which initially she was so called. Initially, I though this was a mistake, and
indeed likely so, as it would be most unlikely a modern-day bookseller with no interest
in Eagle-Clarke would be privy to such detail. However, perhaps it is indeed
true! Who knows?
SMP Book 1.
Cambridge University Press 1965 (6 August 1994)
First , I place all my SMP books under a single grouping, as ‘SMP’, for the sake of convenience of reference.
There seem to be many different editions and contributors to various books, the
machinations of which I lack the time and desire to unravel, hence the en masse
recording here. Of note is that this was the maths books series I studied
during my school days (how I would love to see this now!), and of which I
vaguely recall a mild interest in tessellation than in other aspects, but this
is indeed so vague as to possibly being a false memory. Of note is that Escher
is mentioned, but not illustrated in any book. Generally, tessellations
Within a chapter on area, and
sub Patterns (tessellations) 159-163, of basics. P. 163 appears to have been
the source for some SMP-inspired
studies of November 1987. Of note is a tiling later used by myself for a bird
tiling, the tilings of which was used again in Book B.
SMP Book 3. Cambridge University Press 1976 (c November 1995)
No tessellation (Hardback).
SMP Book 4. Cambridge
University Press 1979 (6
No tessellation (Hardback). P.
266 has a clown figure of a five-fold nature which I studied in 1989. Parabolas
SMP Book B. Cambridge University Press 1974 (29 August 1993)
(A series of eight books, A-H, for CSE. SMP 1-5, is for O-level)
In contrast to other books in
the series, of a substantial reference to tessellations, in relative terms, with
a prelude on ‘Tiling Patterns’, albeit of a basic nature, of first premises, pp.
1-5, and a dedicated Chapter 2, Tessellation, pp. 13-22. By far, of the SMP
series, this book is the most substantial regarding tessellations, albeit this
is in relative terms. Diagrams of particular note include p. 18, Figs. 11a, b. Av
note is a tiling later used by myself for a bird tiling, the tilings of which
was used again in Book 1, p.163, and a clamshell, p. 19.
SMP Book F. Cambridge
University Press 1970 (10 February 1994) (A series of eight books, A-H, for
CSE. SMP 1-5, is for O-level)
SMP Book H. Cambridge University Press 1972. (16 October 1993)
Minor tessellation, pp. 83-84,
with a P. Murphy chicken-like motif p. 84, within a chapter on Geometry, pp.
SMP Book T. a 9
December 1986 reference.
SMP Book X. Cambridge University Press 1973 (25 August 1991)
A follow-on from books A-H,
for O-level. No tessellation.
SMP Book Y. Cambridge University Press 1973 (25 August 1991)
SMP Book Z. Cambridge University Press 1974 (25 August 1991)
SMP Teacher’s Guide for Book X. Cambridge University Press
1974 (25 August 1991)
SMP Teacher’s Guide for Book C. Cambridge University Press
1971 (18 April 1993)
SMP Book X. Cambridge University Press 1975 (not dated)
SMP 11-16 R3. Cambridge
University Press 1989 (14
Impossible objects 116-117
‘Penrose-like’ stairs page 125. No tessellation.
Smullyan, Raymond M. What is the Name of this Book. ils
Riddle of Dracula and other Logical Puzzles. Prentice-Hall Inc. 1978 (date
semi legible – 2000?)
271 popular logic puzzles in
four parts. Of minor recreational interest, nothing more. Has occasional
stories on mathematicians. Overall, I have limited patience with the genre.
Sommerwell, Edith. A Rhythmic Approach to Mathematics.
Classics in Mathematics Education, Volume 5.
This book is a reproduction of
a monograph written in 1906 to advocate the use of curve stitching in the early
school years. The book was originally accompanied by a set of punched cards
depicting geometric shapes; each card could be used in the construction of many
varied designs. The book's preface is written by Mary Boole, to whom the
technique is attributed by the author. Both the preface and the text itself
praise the use of curve stitching as promoting both aesthetic satisfaction and
subconscious awareness of pattern, harmony, and relationships among objects.
The importance of using pleasing colours and of allowing the child to work out
his own rules for stitching is stressed. Methods of developing the curve of
pursuit, the parabola, and other curves are described. Many figures
illustrating the principles used and plates displaying complex designs
completed by children of various ages are included. (SD)
Springett, David. Woodturning
Wizardry. Guild of Master Craftsman Publications Ltd 1973. (18 May 2014)
Although strictly not a
mathematics book, included nonetheless as it has certain crossovers, albeit
most tenuous indeed. I seem to recall John Sharp quoted this author in an
article, and so I was ‘primed’ to notice this. This includes a historic
polyhedral instance from a book I was unfamiliar with: Manuel du Tourneur, 1816 by Hamelin Bergeron. Also, it reveals how
the seemingly impossible ‘arrow through bottle’ was achieved, pp. 54-63. Much
of interest in a generalised sense with polyhedra carving.
later colour edition was subsequently seen in both Cleethorpes and Grimsby
Staněk, V. J. Skjønnhet
in Nature. Artia, Prague
1955 (c. 1995-2000). Oversize.
Not really a maths book, has
occasional pattern by default.
Stannard, Dorothy (Editor). Egypt.
Insight Guides. Fifth edition 1998, updated 2000, reprinted 2002) first edition 1987, not seen (obtained 13
April 2013, Cleethorpes library sale. First
saw 5 May 2011, Grimsby
Although not a maths book per
se, has an instance of the Cairo
tiling, and so is thus included here. Has Cairo
tiling page 171, clearly displayed, outside a mosque in the City of the Dead.
This is of note as the first pictured reference seen by myself, although
subsequently I have found other, and indeed earlier instances. Somewhat
ironically, given extensive searching in maths books this reflects badly on me,
it being under my nose at least since when the library obtained, in 2001, but I
simply didn’t think of a possibility of it being in travel guide books.
Steadman, Philip. Vermeer’s Camera. Uncovering The Truth
Behind the Masterpieces. Oxford
University Press 2001 (26
Camera obscura conjectures.
Steinhaus, H. Mathematical Snapshots. (Third American
edition, Revised and Enlarged, with a new preface by Morris Kline). Oxford University
Press 1983. (30 April 1994)
Many aspects of recreational
interest. Chapter 4, tessellations pp. 75-83.
Stephens, Pam. Tessellations: The History and Making of Symmetrical
Designs. Crystal produksjoner (19 March 2010)
Juvenile content, despite the
serious title, of only 40 pages. Stephens apparently wrote the entire text,
with the artwork (tessellations) by Jim McNeil. Pages 1 and 2 cut out, hence
this lacks bibliographical detail.
Stevens, Peter S. Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions. The MIT Press, Cambridge, Massachusetts and London, England). First printed 1981, Third printing, 1987 (c. 15 December 2007, through receipt). First saw 4 October 1990
First saw 4 October 1990 (ordered through the library), this sparking a concerted study of the day, throughout the month of October. Illustrated throughout with various Escher periodic drawings. Occasional Cairo tilings arising from my studies, although not directly from the book itself. A most pleasant read, with a crystallographic leaning, best described as a compilation (as the author, an architect, admits) of tiling and patterns throughout the ages. A feature, scattered liberally throughout the book, is of geometric Escher-like tessellations, of which I believe acted as the moving spring of my own. These would appear to be by Stevens, albeit there are doubts here, as this is not made explicit. In the preface Mollie Moran is credited with drawing most of the illustrations, hence my uncertainty.
If there's one criticism, the illustrations need more detail; sometimes nothing at all is given, whereas with others there is only a bare minimum.
Of direct interest:
Houndstooth tiling (not standard model), pp.195-196. Said to be from Sandwich Islands, of which likely this refers to Owen Jones’ Grammar (who is mentioned in the bibliography).
Dogbone tiling, p. 294, Arabian.
————. Patterns in
Nature. Penguin Books 1977. First published 1974 by Little, Brown & Co.
(16 September 2007)
Although not a maths book in
the conventional sense, included nonetheless as it is of interest. Tiling is
mentioned only briefly, in Chapter 1, with a small section on polyhedron and
mosaics, pp. 11-16. Even so, some innovations here. The semi-regular tilings
are presented as according to the number of corners, of which off hand I don’t
believe I have seen as in this particular presentation.
Stewart, Ian. Concepts of Modern Mathematics. Penguin
Books 1982. First published 1975 (16 May 1999) (17 November 1994 and 24 August
Of limited interest, with somewhat
technical, advanced concepts way beyond me. 339 pp. paperback. Topology,
Chapter 10 pp. 144-158. No tessellation, Escher. No plans (2018) to re-read.
————. Game, Set and
Math. First published 1989. SEEN
From a reference on an old
cardboard ring binder, of 3 May – 21 days library book. The content is now
(2018) long forgotten. I do not recall
any studies arising from this.
. ————. Nature’s Numbers. Discovering Order and Pattern
in the Universe. Weidenfeld & Nicholson London 1995 (7 November 1998)
Science masters series.
Popular account, but of
general interest only, no tessellation.
————. Does God Play Dice? ils New
Mathematics of Chaos. Penguin Books 1997. (Date not given).
Of limited interest.
————. Taming the Infinite. First published 2008 by Quercus, 2009 paperback (21 February 2015)
finding. Although the subject matter is mostly beyond my understanding, it
contains the occasional snippet of interest. For instance, fuel efficient planetary
probe orbits by Edward Belbruno. In all my time in astronomy, I was unfamiliar
with the fuel concept as outlined by Belbruno p. 372, and indeed of himself!
Escher p. 223, a single line mention in the context of hyperbolic geometry. aucun
Stewart’s Cabinet of Mathematical Curiosities. Profile Books 2008 (4 June
————. From Here to
Infinity. A Guide to Today’s
University Press 1996. First
published 1987 (17 June 2012)
Largely popular account of
hard to understand concepts. Quiscrystal tiling p. 101-103. Chapter 12, Squaring
the Unsquarable, Geometric Dissections pp. 168-171. No references to Escher,
tessellation or tiling. Shortage of time (2018) forbids a re-read.
Stewart, Ian and Martin Golubitsky. Fearful Symmetry: Is
God a Geometer? University Press 1993
Occasional Escher pictures,
Circle Limit IV, p.45, Lizards 237; Penrose tiling p. 95, Kepler’s Aa to Z
patch, p. 96; Pólya diagram p. 239, with Pólya’s annotations, but generally all
these references are in passing only.
Stewart, Desmond. tôt
Islam. Great Ages of Man. 1967, Time-Inc. (First saw, or at least recorded
13 September 1987, and again studied 9-11 August 1988) recording as seen Cental
library and Willows library? Not in Possession. Saw at Internet archive 1
Part of a 20-book Time-Life
series. Not on tilings as such, but of course with many side references. Only
tiling aspects of interest pp. 150-151 and 156-157, with double page spreads.
————. and the editors of the newsweek book division. The Alhambra.
TBS The Book Service Ltd; First printing 1974, 1976 (Internet Archive 1
Recorded on a menu card, c.
September 1987. A single study of 11 July 1988 study.
General discussion on the Alhambra without a
dedicated study of tilings per se. Many pictures have not been seen before.
Although tilings do appear, this merely illustrates the discussion. Of most
interest pp. 15, 33, 73, 101, 125, 183, where a tiling is shown full on, as a
square each time.
Sutton, O. G. Mathematics in Action. G. Bell and Sons
Ltd 1966 (24 October 1996 or 1998)
Semi-popular, although tending
towards the advanced.
Sykes, Mabel. source
Book of Problems for Geometry. (subtitled as … Based upon Industrial Design and Architectural Ornament) Dale
Seymour Publications. Originally published 1912 by Norwood Press, Norwood, Mass.
(1 March 2012)
From a reference in Britton. qui
such, I consider this book poorly titled in the (obviously modern day, but year
not stated) reprinting, as the cover does not give the full title to adequately
describe the contents; only with the full title does it make sense.
is very little tiling here per se; rather, the book is concerned with designs
in a variety of given shapes, such as church windows. And what tiling there is,
is from other sources, rather than from Sykes herself. Part 2 is on tiled
floors, pp.13-22, and parquet floor designs. Even, there are some tilings I
have not seen before, such as p. 19, of regular octagons and isosceles right
triangles. Throughout the book, exercises are given, most of which are beyond
me, not that I have the time to do these in any case….
Tallack, Peter, ed. Science
Book. Cassell & Co., 2001 (30 May 2015)
Overweight coffee table book,
occasional maths. Escher’s print Möbius
Strip II s. 144. Reference to Arnold (Nol) Escher, p. 206 as regard mountain
formation. s. 482 Quasicrystals.
Tammadge, Alan; Star, Phyllis. A Parents’ Guide to School
University Press 1977 (4
Tapson, Frank. Oxford
Study Mathematics Dictionary. Oxford University Press, First published 1996,
fourth edition 2006 (21 February 2015)
Chance finding. Intended for a
11-16 audience, albeit even here, much of this remains obscure. Gives simple
definitions of mathematical terms. Of perhaps most note is a Cairo tiling (not
attributed) on p. 139.
Taylor, Don and Leanne Rylands. Cube Games. 92 Classic
Games, Puzzles & Solutions. First published in Great Britain by Penguin
Books 1981 (my copy). First published in Australia by Greenhouse Publications
Pty Ltd 1981. (20 June 1993)
Small format paperback, 50 pp.
In short, a how-to on Rubik’s Cube, published with many others at the height (1981)
of the craze. Quite where the ‘92 classic games’ is derived is unclear; it’s
simply a monologue on Rubik’s Cube. This is perhaps better than most of the
day, at least in theory, with colour diagrams, which is surely better than line
diagrams with initial letters from colours. Taylor and Rylands are both
(mathematical) Australians, hence the Australian publication.
books are essentially in my past now (2018). There is simply a lack of time to
Taylor, Don. Mastering Rubik’s Cube. Penguin Books
1981. (29 August 1993)
Very small book.
Thé, Erik, Designer. The Magic of M. C. Escher. Joost
Elffers Books Harry N. Abrams 2000. Foreword by W.F. Veldhuysen. introduction
by J. L. Locher. (2 September 2004)
A major work on Escher, one of
the ‘core value’ books. Oversize, with numerous gatefolds. The premise is
visual rather than text. Indeed, there is no text save for accompanying quotes
from Escher in various letters. the larger format thus enables the prints and
drawings of Escher to be more properly shown at their larger sizes. Has
occasional sketches that up to this date, I had not seen before, such as pp. 72-73,
96-97, 107, 111, 113, 150-151, 163, 166-167, 177, 179, 181, 184, 187-189.
Surprisingly, there is very little tessellation in the book; it’s mostly on
prints without the tessellation element, and certainly no concept sketches, at
least worthy of the name.
Has a serious bibliography, titled
‘Selected Bibliography’, p. 196, which is a facsimile, reference for reference
(checked 6 October 2016) of Locher, Escher
The Complete Graphic Work.
The Yellow Book. Some
early designs of later 1890s that can be interpreted as of a tessellation
As given by Andrew Crompton.
Thomas, Frank and Ollie Johnston. The Illusion of Life. Disney Animation. Disney Editions N York 1981 (5 December 2009)
Obtained solely due to Craig
Kaplan’s reference to it in his thesis (and reference to it is as the likely
anonymous reviewer of my Bridges paper, as regards the ‘staging principle’). qui
such, as regards tessellation aspects re ‘staging’, I do not find anything of
relevance. Undoubtedly, a good book in its field, but not for tessellation
Thompson, D’Arcy Wentworth. On Growth and Form.
Abridged edition by J. T. Bonner. Cambridge
University Press. 1975
(13 July 2009). First published 1917, Cambridge University Press
A single-sheet study of this
is dated 31 March 1988, of which by the page numbers quoted is clearly of an
edition by Thompson (1,116 pp.), rather than the abridged (346 pp.) by Bonner.
Likely this was by following a reference somewhere (possibly The Art of Microcomputer Graphics for the BBC Micro/Electron which quotes this), but if so is long forgotten. I do not recall the circumstances of whether
this required ordering; I suspect yes. However, as regards tiling, it is a
relative disappointment, with only p. 505 studied, albeit as it not as such on
the subject, one would thus not expect such matters to appear, and if so, only
in passing. Simply stated, an inconsequential study.
From Wikipedia: On Growth and Form is a book by the Scottish
mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long
– 793 pages in the first edition of 1917, 1116 pages in the second edition of
1942. The book covers many topics including the effects of scale on the shape
of animals and plants, large ones necessarily being relatively thick in
shape; the effects of surface tension in shaping soap films and similar
structures such as cells; the logarithmic spiral as seen in mollusc
shells and ruminant horns; the arrangement of leaves and other plant parts (phyllotaxis);
and Thompson's own method of transformations, showing the changes in shape of
animal skulls and other structures on a Cartesian grid.
The work is widely admired by
biologists, anthropologists and architects among others, but less often read
than cited.(1 )Peter Medawar explains
this as being because it clearly pioneered the use of mathematics in
biology, and helped to defeat mystical ideas of vitalism; but that the
book is weakened by Thompson's failure to understand the role ofevolution and
evolutionary history in shaping living structures. Philip Ball and Michael
Ruse, on the other hand, suspect that while Thompson argued for physical
mechanisms, his rejection of natural selection bordered on vitalism….
Thorndike, Joseph J. (Editor-in-Chief). ‘Escher's Eerie
Games’. Horizon 8, no. 4 (1966):
110-115. (24 May 2014)
First, note that as such, the
article, in a ‘general arts’ book published three-monthly, is not credited with
an author (other articles in the same book are the same.)
As Thorndike is the main
editor, I this file under his name for wont of anything better. Does anyone
know who the author is?
A brief essay on Escher, illustrated with eight prints, Hand with Reflecting
Globe, Tetrahedral Planetoid, Magic Mirror, Horseman, Tower of Babel, Three
Intersecting Planes, Waterfall, Belvedere. The text is most lightweight indeed,
with a picture bias; no real insight is offered by whoever wrote this.
Thornburg, David D. Exploring
Logo Without a Computer. Addison-Wesley Publishing Company 1984 (27 June
Being on a popular computer
program of the day, Logo, now some thirty years later somewhat dated. Note that
the book is not just about tessellation. Of most interest, relatively, is Chapter
V, on Tiling and Symmetry pp. 59-100.
Escher’s Pegasus p. 73, Shmuzzle pp. 74, 99. Pentagonal tiles pp. 66, 67, but seen
previously. Author’s own (poor) dog tessellation p. 77. Of no consequence.
Thyer, Dennis and John Maggs. Teaching Mathematics to Young Children. Holt, Rinehart and Winston,
Second edition 1981. First published 1971 (27 July 1997)
On teaching Infants (rather
than a textbook). Of limited interest. Tessellations are briefly mentioned and
illustrated 84-85, 95, 209, 213, 217, but are not of any significance.
Todd, Audrey. The Maths Club.
Hamish Hamilton London.
First published 1968. (26 September 1991
a 9-16 age range school maths club. No tessellation. Chapter 4 of a substantial
nature, pp. 43-65, ‘Curve Drawing and Stitching’ may have influenced some c.
1986-1987 studies. Chapter 5, pp. 66-78 ‘Geometrical Solids’ as well.
Tolansky, S. optique
Illusions. Pergamon Press 1964. (26 July 1997)
scholarly account in a popular manner (in contrast to mostly others, of a
lightweight nature). No maths at all.
Tóth, Fejes L. Regular
Figures. Pergamon Press 1964 (12 December 2010), partial copy, of Chapter 1
up to p. 43…
Largely theoretical. Mostly
concerning group theory, which is out of my remit. Occasional tiling. Escher
mention p. 39. Tilings Plates 1-3. As such, of what I have seen (Chapter 1 Plane
Ornaments only), of no consequence (likely, the book is even more obscure in
Townsend, Charles Barry. ils
World’s Greatest Puzzles. 1996. Quality Paperback Book Club New York. (3 June 2007?)
(The date stamped year has faded in the book). An anthology of four books: The World’s Most Challenging Puzzles; World’s Most Baffling Puzzles; World’s Greatest Puzzles; World’s Most Incredible Puzzles
a general statement, the puzzles are of a Dudeneyesque nature, in both style
and substance (with black line drawing reminiscent of the period, early 1900s).
Very little is said of the source of the puzzles. ‘Professor Hoffman’
(primarily) and Sam Loyd gets a credit, and no one else. Looking at the
puzzles, albeit admittedly briefly, many of these are well-known, of which it
is unlikely that there is too much, if any, in the way of originality by
Travers, James. Puzzles and Problems. The Education
Outlook, 145, 1933. WANTED
————. Puzzling Posers. Londres
George Allen & Unwin Ltd, 1952. WANTED
Tufnell, Richard. Introducing
Design and Communication. 1986 Nelson Thornes Ltd
(c. 14 April 1987) SEEN, BUT NOT IN POSSESSION.
minor tessellation studies, nothing in the way of originality.
Turner, Harry. Triad
Optical Illusions and How to Design Them. Dover Publications 1978
72 pp. Drawn to my attention
de Alan Bridges of art college. First
saw 22 February 1993, where I seemingly borrowed and photocopied the entire
book the next day, upon which I then studied on the sheets themselves. I canot
recall if I have subsequently obtained the book. I cannot find it if so; I get
mixed up with other similar Dover publications by Locke and Willson.
Tyler, Tom. British
Jigsaw Puzzles of the 20th Century. Richard Dennis 1997 (22 March 2014)
Of jigsaw puzzle interest. Même si
by its nature this is not a maths book, as it includes two aspects of tiling
(albeit brief, pictures only) I nonetheless include here for the sake of
convenience. These references on p. 110 are Penrose’s ‘Perplexing Poultry’ and
a new name to me in regards of cluster puzzles, George Luck, who shows a
‘animal map’ of the British Isles. Upon following this up, I see that he has
many other examples of (likely independent discovery) cluster puzzles, of a
decided simplified nature, of which they can be described as relatively ‘pleasing’,
but certainly not outstanding.
An excellent piece of
research, one of the few ‘must have’ books. Among the jigsaw puzzle aspects of
Hamley’s (in regard of a
newspaper report of one of the earliest cluster puzzles), in which there is
scant detail of this source. P. 8 includes a box, described as ‘THE GREAT
Society Picture Puzzle’. A brief, three-line discussion of this is given in
Chapter 9, p. 127 Coronation puzzle of HM King George V and Queen Mary. An open
question is to whether Hamley’s made this themselves, or outsourced.
Treadle history, p. 16,
described as ‘in use by 1900’.
As such, there is no apparent
mention of their connection with jigsaws on the company history, going back to
1760 (Wikipedia, and elsewhere)
surprisingly so for such a
major company. Wikipedia: Hamleys is the oldest and largest toy shop
in the world and one of the world's best-known retailers of toys. Founded by William
Hamley as "Noahs Ark" in High Holborn, London, in 1760, it moved
to its current site on Regent Street in 1881…. . Dreweatts gives
‘label of Hamley Bros. on sliding lid, 1909’. £150 – £200.
A company history is given at http://www.hamleys.com/explore-life-history.irs,
albeit this is most lightweight indeed.
Varnedoe, Kirk. Vienna
1990 Art, Architecture & Design. New York: The Museum of Modern Art,
1986. (8 September 2017)
From a reference in Visions of Symmetry, p. 42 re Moser designs,
where Schattsneider states:
… Only recently have Escher’s designs been compared with Moser’s patterns;
for instance in a 1986 essay by Marianne Teuber in M.C. Escher: Art and Science
and in the 1986 exhibition catalog Vienna 1900 by Kirk Varnedoe.
A major disappointment! qui
such, I am more than a little under whelmed with such a brief references of no particular
insight of just a single sentence; kanskje
influenced by Tuber’s in-depth essay, I was expecting a like treatment, but this
piece (if it can be called that) is emphatically not so. Though the book may
come in useful in a generalised sense, as to Moser, this is not why I obtained
it! I was hoping for more Escher comparisons from Varnedoe, of an essay.
As a bonus, but nothing more,
there is extensive discussions on Moser, both focussed and scattered throughout
the book, but disappointingly nothing at all on Erwin Puchinger.
Valette, G. Les
Partages d’un Polygone Convexe en 4 Polygones Semblables au premier (in
Van Delft, Pieter, and
Jack Botermans. Creative Puzzles of
the World. Harry N. Abrams. Edition? First seen around 15 June 1987, the
first recorded date of study.
Vecht, N. J. van de. ils
grondslag voor het ontwerpen van vlakke versiering (Fundamentals for the
Design of Surface Ornament), Rotterdam, 1930. From a refence in The World of
M.C. Escher, p. 22 WANTED
Veldhuysen, W. F. (the author is unclear; Veldhuysen wrote
the foreword, hence placed accordingly). M.
C. Escher International Ex libris Competition. Homage to the Dutch Graphic
Artist M. C. Escher. 1998? (Bridges Leeuwarden 2008 free)
On a Escher theme of ex
libris, on a competition marking the 100e anniversary of his birth.
This collects all of Escher fifteen ex libris works (pp. 6-20), with an
pleasing, insightful essay on these by Jos van Waterschoot, along (pp.21-23)
with the best of the competition. Only two names are known to me, Kenneth
Landry (p. 57), with his enigmatic repeating portrait of Escher, and István Orosz
(p.33). Many examples of ex libris prints from artists in tribute to Escher are
shown. I do not generally find favour with most entries; however, an honourable
exception is Frank-Ivo van Damme (p.47), with an original Escher-like
tessellation/composition, of a human figure.
Vermeulen, Jan W. Escher on Escher. Exploring the
Infinite (original title, or
published as Het Oneindige English Translation by Karin Ford).
Harry N. Abrams, New York
1989.) 29 May 1991
Escher's writings collected.
Vorderman, Carol. How Maths Works. Dorling Kindersley,
Tessellation 130-131, Polyhedron
————. Help Your Kids
with Maths. Dorling Kindersley, 2010. (2 July 2016)
Covers the basics, but even
here, I’m struggling in more places than I care to (pinlig) list…
Wade, David. Crystal & Dragon. The Cosmic Two-Step.
Green Books 1991 (27 November 1993)
————. Geometric Patterns & Borders. Wildwood House Ltd. 1982 (16 September 1995)
The premise is of a geometric pattern book, with line drawings and colouring (in black and white) from various countries around the world. Text is seemingly purposefully kept to a minimum at the beginning of the book. The book is (regrettably) not paginated, but rather is ordered by diagram numbers. No bibliography. Has many interesting designs, worthy of study, of which I return to at intermittent intervals. Countries of origin generally accompany the diagrams, but no other detail, which is frustrating where more specific detail is sought. Nonetheless, even with shortcoming of presentations, the book is a veritable visual feast, to be returned to time and again. No Cairo tiling as such.
Diagrams of interest include:
193, double axe head tiling
194, Cairo tile-related bowtie tiling.
260, houndstooth, stated from Hawaii, likely referring to the Owen Jones reference in Grammar of Ornament, p. 15. However, Wade’s instance is different in proportion, based on an isometric grid.
333, Cairo tile and regular hexagon in combination.
383, houndstooth in nature, of a ‘pixelated weave’ type, and is briefly discussed in the introductory text, ‘… from African basketwork…’. However, beyond this, no specific detail as to source.
555, houndstooth as a frieze.
————. Pattern in Islamic Art. Studio Vista 1976 (12 March 2010)
Primarily a diagram led book,
with little text. The diagrams are not sourced. No Cairo. The first half of the
book s of more interest than the second. The second is more concerned with
complex patterns, and their construction. Of interest: pp.10-11, square root of
2 and 3 triangles, and rectangle thereof. ‘Fused Cairo’ p. 20, octagon based
patterns p. 34 and others.
Wade, Nicholas. Vision,
Illusion and Perception Art and Illusionists. Springer 2016 (2 March 2017)
Complementary copy from
Springer. Popular account. Lots of interest. Chapter nærmere bestemt on tiling, with
frequent references to Escher.
Wallis, Denis (Principal writer). Reader’s Digest Why in the World? 1994 First edition, The Reader’s
Digest Association Limited (10 August 2015)
One minor reference to Escher,
s. 87, with Waterfall and general text.
Walker, Michelle. ils
Complete Book of Quiltmaking. Guild Publishing London Book Club edition
1989. First published 1985. First saw 1 May 1987 (15 May 2015)
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed, it is one of the best books, in
relative terms, there is on the interrelation between the two, and indeed led
to extensive studies of the day (1987, as indeed with other patchwork books).
However, now, and for some considerable time, the nature of the material is considered
hardly worthy the time originally devoted to it.
in the bibliography, Walker quotes David Wade (2) and Johannes Itten, not to
mention Jinny Beyer.
The Mirror Puzzle Book. Tarquin
Publications, 1985 (30 January 1999)
Juvenile, of no interest.
Boxes, Squares and Other Things. A
Teacher’s Guide for a Unit in Informal Geometry, NCTM. 1970 PDF (February 2018)
For children 8-11.
Tessellations pp. 57-59. Has a most intesting biblography, with some tesellation references not seen before!
Wark, Edna. The Craft
of Patchwork. Saw 7/8 July 1987
Although obviously not a book
on mathematics per se, it is nonetheless included in this listing as it has
interesting pattern aspects, and indeed, led to minor studies of the day
(1987), of just two (dual-sided) pages as indeed with other patchwork books.
However, now, and for some considerable time, the nature of the material is considered
hardly worthy the time originally devoted to it.
Washburn, Dorothy K. and, Donald W. Crowe. Symmetries of
Culture. Theory and Practise of Plane Pattern Analysis. University of Washington
Trykk. 1988 Second Printing 1992. (30
Simply stated, although widely
quoted in tiling literature, in truth there is very little here for the tessellator.
It mostly consists of notation systems for pattern, not necessarily tessellation.
P. 7 gives the first likely apparent
reference in print to the term ‘counterchange’, by A Text Book Dealing with Ornamental designs for Woven Fabrics, off
Stephenson and Suddards, 1897, p. 18. 158 paving tiles from fourteenth century,
France. s. 172, stylised swans from Escher, p. 206 arrowhead tiling variation,
s. 219 Escher's lizards, p. 232 Chinese traditional design.
Weaire, Denis. ils
Kelvin Problem. Taylor & Francis, 1997. WANTED
Of note is that in the
preface, by Charles Frank, in so many words surely is discussing the Cairo
tiling, seen at Glasgow Physics lab!
Wells, A. F. The Third
Dimension in Chemistry. University Press, Oxford, 1956 (8 February 2016?).
Wildly quoted in tiling
mathematics despite being a chemistry book! Cairo tilings pp. 24-25, in the
context of Laves tilings, although not named as such (8 February 2016). C'est
pleasing as Wells mentions, p. 24, the aesthetics, with ‘… a very elegant
arrangement of pentagons…’.
Wells, David. Hidden Connections Double Meanings. Cambridge University Press 1988. (30 April 1994)
A somewhat hard to describe
book, loosely on ‘popular geometry’, with a subject followed by answers. Pp. 22-23
dissections of dodecahedron into rhombs; tiling pp. 24-26, 45, 57, 121.
————. The Penguin Dictionary of Curious and Interesting
Geometry. Penguin Books 1991. (30 April 1994)
Cairo line drawing, and discussion p. 23.
————. The Penguin Book of Curious and Interesting Puzzles.
Penguin Books 1992. (30 April 1994)
This is best described as a
compilation of puzzles from a variety of other authors (as noted in the
acknowledgements), notably by Dudeney and Loyd. Nothing of originality from
————. The Penguin Book of Curious and Interesting Numbers.
Penguin Books 1987 (31 March 1995, first saw 16 June 1990)
Popular account of properties
of numbers, of the same premise of Neil Sloane, but much more accessible.
————. You Are A Mathematician. Penguin Books 1995.
(23 April 1998)
The book is somewhat mistitled,
as it is essentially a (popular) book on geometry. Has only occasional tessellation,
on pp. 246 and 319, but of a lightweight treatment.
Wenninger, Magnus J. polyhedron
University Press 1989. (3
Foreword by Coxeter. Popular
account, of 119 polyhedra. Discusses colouration (although the book is in black
and white) and history.
————. Polyhedron Models for the Classroom. National
Council of Teachers of Mathematics (NCTM) 1986 (3 June 1993)
Werneck, Tom. Mastering the Magic Pyramid. The Secrets of the Pyraminx (sic) Unlocked.
Evans Brothers Limited 1981 (11 June 1994)
Small format paperback, 112 pp,
with instructions for solving the Pyraminx, a Rubik’s cube-type puzzle, published
at the height of the Rubik cube craze. The puzzle is more properly known as the
Pyraminx. Originanally, I thought this was Rubik-inspired of the day until
latterly re-reading the book and seeing the Wikipeda entry:
Fom Wikipedia: The Pyraminx was first conceived by (Uwe)
Mèffert in 1970. He did nothing with his design until 1981 when he first
brought it to Hong Kong for production. Uwe is fond of saying had it not been
for Erno Rubik's invention of the cube, his Pyraminx would have never been
On Tom Werneck, of whom I was
unfamiliar (Form Boardgamegeek): Tom Werneck (born 1939) is a pioneer of board game journalism in
Germany, who wrote more than 5000 articles for newspapers, journals and radio.
In addition to that, he is a game designer and author from Haar, Bavaria,
Germany. He is a co-founder and former member on the jury for the Spiel des
Wesley, R. (ed.) Mathematics for All. Odhams Press
Ltd 1954 (18 March 1994).
Very much of its day, with
much laborious calculation.
Weyl, Hermann. Symmetry. Princeton University
Press, Princeton, New Jersey. 1989 (11 June 2007)
Although this little book is
much praised in the tiling world, I must admit that for my purposes I was a
little disappointed with it. Certainly, it is of interest, but the audience it
is intended for is not clear; there are both recreational and academic
instances of study. Tiling as such is at a minimum, subsumed under ‘Ornamental
Symmetry’. Of note is that an earlier edition, in Russian, of 1953? shows
Escher’s Lizards, the first such usage his work as cover art.
Wheeler, Francis Rolt- (Managing Editor). The Science
History of the Universe. Mathematics. Vol. VIII. In ten volumes, Volume
VIII, Mathematics. The Waverley Book Company Limited Copyright 1909 and 1911
(Date of publication not stated)
Small format hardback.
Semi-popular,semi-scholarly account of mathematics. Of most interest is
geometry, Chapter 5, pp 107-154, with
Kepler pp. 112-113, Perigal dissection of Pythagoras diagram. s. 114, Designs
on Tombs of Bernoulli, Archimedes, p. 137. Liberally illustrated, but a bit too
advanced for me. No tessellation,per se, although there is ‘tessellated muliplication’,
s. 44, of which I was unfamilar with.
Looking on Google, I cannot find any other instances of this description.
Astronomy, by W. Kaempffert; introduction by E.E. Barnard.–II. Geology, by
H.E. Slade and W.E. Ferguson.–III.
Physics, by G. Matthew. Electricity, by W.J. Moore.–IV. Chemistry, by W.A.
Hamor; introduction by C. Baskerville.–V. Biology, by Caroline E.
Stackpole.–VI. Zoology, by W.D. Matthew. Botany, by M.E. Latham; introduksjon
by W.T. Hornaday.–VII.
Anthropology, by F. Rolt-Wheeler. Medicine, by T.H. Allen; introduction by F.
Starr.–VIII. Pure mathematics, by L.L. Locke. Foundations of mathematics, by
C.J. Keyser. Mathematical applications, by F. Bellinger; introduction by C.J.
Keyser.–IX. Art, by B.S. Woolf. Literature, by F. Rolt-Wheeler; introduksjon
by E.J. Wheeler.–X. Schools of Philosophy, by C.G. Shaw. Sociology and
political economy, by L.D. Abbott. Ethics, by F. Rolt-Wheeler; introduction by
Whistler, Rex and Laurence Whistler. AHA. First published 1948 again 1978. John Murray (23 September
Chance finding. Not strictly
mathematical. Of topsy turvey heads, an early instance (although not the first)
in the field of such double imagery. Relatively lightweight, of 21 images. ils
images are by Rex, with accompanying verse by Laurence, his brother. Some are
better than others.
that although not ‘officially’ accompanying the book, inside was a small
booklet of a related theme, ‘Turn Me Round’, with 18 images published by Tobar
Limited, Norfolk (said to be 1997) from Dreh’ mich um, rund herum’ by Otto Bromberger,
published in Germany in the late 1890s. This was without any text whatsoever,
not even a caption or paginated.
White, Gwen. A World of Pattern. John Murray 1957.
(23 September 1996? The last digit is unclear).
Juvenile, mostly patterns in
the real world. Occasional tessellation.
A Guide for Artists, Architects and Designers. 1982. Batsford Academic
and Educational Ltd.
Recommended by art class tutor
Peter Bendelow, c. 1983.
White, William F. A
Scrap-Book of Elementary Mathematics. Chicago The Open Court Publishing Co,
1908 (Downloaded from Project Gutenberg 8 June 2015)
Lots of recreational aspects,
with most of interest to me: geometric dissection pp. 91-99, tiling p.100,
four-colour theorem p. 120-121.
Whitelaw, Ian. un
measure of things (sic). The story of measurement throughout the ages.
David & Charles, 2007. (5 August 2018)
160 pp, small format hardback.
Popular account, of 11 chapters, in bite size.
Whitehouse, F. R. B. Table
Games of Georgian and Victorian Days. Peter Garnett Ltd, London, 1951 (27
November 2018). (PDF)
Of game interest. In-depth
treatment, although of a popular nature. Liberally illustrated. Twelve chapters, of particular interest
Chapter X, ‘Jig-Saw Puzzles’, pp 84-85, on John Wallis, albeit lightweight in
depth. Book quoted in Hannas, The English
Jigsaw Puzzle. First saw on Giochidelloca Italian site.
Williams, Anne D. ils
Jigsaw Puzzle. Piecing Together a History. Berkley Books, New York, 2004 Foreword
by Will Shortz (17 July 2014).
Although not strictly a maths
book, included here as it has certain crossovers to my recent interest in
cluster puzzles. All pages and photos are in black and white. Some outstanding
scholarship is displayed. One of the few ‘must have’ jigsaw books.
perhaps most interest is that of Margaret Richardson’s entry, of pp. 55-57, 59,
and one of the unnumbered plates, ‘plate 8’. Pp. 55-56 gives a detailed
account, whilst pp. 57, 59 are mentions in passing. Plate 8 shows a picture of ‘Kentucky
Belle’, of 908 pieces. No other puzzles are mentioned by name; certainly no
mention is made of ‘A Bad Dream’. Pieceful Solution (Shumaker and Power) plate.
Escher p.107 (a mention in passing, on Savage), Savage p. 107 and endnotes p.
217. Palmer, or indeed the concept of cluster puzzle beyond Pieceful Solution. Has
an excellent bibliography and endnotes. Includes Richardson’s Kentucky Belle.
Just for general interest, I have a list of Richardson’s puzzles known from
————. Jigsaw Puzzles.
An Illustrated History and Price Guide. Wallace-Homestead Book Company,
1990. (c. November 2015)
Although not strictly a maths
book, included here as it has certain crossovers to my recent interest in
cluster puzzles. The book is more properly described as an American history, as stated in the preface. The price guide aspect
(pp. 326-330) is most minor, and should arguably have been left out of the title;
the book is overwhelming of history puzzles, and not a price guide per se. Minor
references are made to Margaret Richardson, pp. 12, 37, 149, 153. P. 37 is of a
dedicated section. Sam Savage’s Schmuzzles
puzzle p. 325, which mentions a 16-page instruction book of tesselated
(sic) figures that I have not seen.
Williams, Robert. The Geometrical Foundation of Natural
Structure. A Source Book of Design. Dover Publications, Inc. 1979 (3 June
Of most note is a Cairo tiling pp. 38, 204,
in the context of the dual and transfromation between squares and basketweave
tessellations. Quite how best to describe Williiams is unclear. Architect,
designer? He deos not appear to be a mathemtaican per se. Further how much of
the book is original with him is unclear. I suspect, from the books and
articles quoted, that he is borrowing heavily. Of note is that on p. 42 he
quotes the most obscure D. G. Wood Cairo tile reference. Of most interest per
se is Chaper 2, ‘Natural Structure and the Two Dimensional Plane’, on tilings
and circle packings, pp. 31-52.
Willson, John. Mosaic and Tessellated Patterns. comment
Create Them. Dover Publications, Inc. 1983. (30 April 1994)
Slim volume, of just 30 pages.
plate 3. (Neglected, or not noticed, until 7 May 2013!)
Very pleasing indeed, with
many simple, but interesting tilings, and ideas thereof. Discussion of tesellations,
in a simple manner, pp. 1-14, 15-18, these being separated by wirfeame plates.
Studied tessellating letters p. 15?
Wilson, Eva. Islamic Designs.
British Museum Press. First published 1988,
Fourth Impression 1992 (3 June 1993)
title is a little less than exact, in both scope and content. The introduction
states the designs are in effect ‘restricted’, from ‘the illuminated Koran’,
‘metalwork’ and ‘pottery’. These are all hand-drawn, rather than of
photographs. The premise is overwhelmingly one of illustration rather than
discussion. Much use is made of material from Critchlow and El-Said &
Parman. As such, it is more of a general introduction to Islamic designs of the
above, rather than of a groundbreaking, definitive work. Given that it
essentially repeats other authors, of no consequence.
Wilson, Robin. Four
Colours Suffice. How the Map Problem was Solved. Penguin Books, 2003.
(6 July 2017)
————. Stamping Through
Mathematics. Springer 2001. PDF (31 December 2015)
Wiltshire, Alan. The Mathematical Patterns File.
Tarquin Publications. 1988 (3 June 1993)
Subtitled as ‘mathematical
patterns in the classroom’, with a leaning towards pedagogue of 10-12 year old
group as far as I can tell. Discusses, or more accurately illustrates, symmetry
(rather than pattern as in the title) in the broader sense, with reflection,
arcs, hexagons, octagons, tessellations, polar graph, quadrants, spirals,
envelopes, overlaps, grids, enlargement, all of no particular merit. Text,
aside from the initial page, is non-existent. No Escher-like tessellation. Not
at all impressed, even for the level it is pitched at.
————. The Geometrics File. Tarquin Publications. 1983
(3 June 1993)
A Tarquin Mathematics
Resources File. Broadly, this is of creating ‘geometrical mathematical
designs’, of a relatively substantial nature, of 79 pages, aimed at a 10-12
year group. Text is at a minimum, with a caption for each aspect under
discussion. Occasional tessellation, pp. 28-29 (one with potential as a human
figure), and pp. 41-42, but it’s not really a book on tessellation as such. aucun
Escher-like tessellation. Of little direct interest now. Also see Wiltshire’s
‘companion’ book The Mathematical Patterns File.
————. Symmetry Patterns: The art of making beautiful
patterns from special grids. Tarquin Publications 1989.
Wood, Elizabeth Armstrong. Crystals and Light. un
Introduction to Optical Crystallography . Speicial edition for Bell
Telephone Laboratories, Inc. (1964). Dover Publications; 2nd edition 1977) (First saw, or at least recorded, 24
September 1987, at college library)
A minor study, in which the crystal studies are
shared with other books of a like nature. Note that the book has been through
variuous editions, although which edition I saw is long forgotten; however,
likely the more substantial Van Nostrand, that than the more slim-line Dover
second edition of 1977. Seen on Internet Archive 29 December 2017.
Wollny, Wolfgang. Reguläre
Parkettierung der Euklidischen ebene durch Undeschränkte Bereiche.
Bibliographisches Institut, Manheim, 1969
From a reference in Tilings and Patterns. Also see four
other articles of Wollny in Geometriae
Wood, Mary. The Craft
of Temari. Search Press 1991 (30 April 1994)
Although strictly a craft book
and not a mathematics book per se, I include this here, as it loosely it is of
a geometric nature. Note that the only reason I got this was that I had seen a
reference to temari balls in M. C.
Escher: Art and Science, pp. 237-238 and colour plate on p. 398, and upon
an opportunity of a book on the subject (at John Bibby’s) I thus obtained. Les propriétaires étaient
my interest in this per se is decidedly minimal; I have no intention of
‘studying’ the subject.
Woodman, Anne; Eric Albany. Mathematics Through Art &
Design: 6-13. Unwin Hyman. (14 August 1995, Hull central library)
Many pages concerning Escher-like
tessellations, beginner’s level, very poor standard indeed, even for children.
Yarwood, A. Graphical Communication. Hodder and Stoughton. 1975 (20
August 1995) Tessellations 190-197
This was first studied between
7, 9, 12 October 1987. Within a ‘graphical communication premise’, this has a
small chapter on tessellations (not Escher-like), titled ‘Geometrical Patterns’
pp.190-195. The tilings are simple, of no consequence.
Young, Jay. The Art of
Science. A Pop-Up Adventure in Art. marcheur
Books 1999. (16 April 2010)
Devised and paper engineered
by Jay Young, written by Martin Jenkins. Oversize. Various illusion/perception
effects illustrated by pop-outs. Also see accompanying booklet, which discuses
the pictures. Minor reference to Escher p. 6, with Relativity print, and book p.
Zechlin, Katharina. Games you can build yourself.
Sterling Publishing Co., Inc. 1975 (23 August 1994)
Mostly board games.
Zusne, Leonard. Visual Perception of Form. New York: Academic Press Inc 1970. (18
From a reference in
Schattsneider and Locher. Of an academic nature, not surprisingly given the
publisher! Large tracts are simply not of direct interest or understandable. A
relative disappointment as regards Escher aspects, with only a few pages
devoted to him, and some in passing, too: pp. 17-19, 55, 114-115, 417. Prints
inkludere Day and Night 18, Circle Limit IV, p. 115. However, the
book itself seems interesting in itself, although academically inclined, but it’s
finding the time to study! Aspects of interest include figure ground, notably
with pp.116-118, where Zusne discusses aspects of the Rubin vase I had not
considered consciously. Pp.300 and 316 are of interest as regards visual form.
Les solides platoniques marchent comme des cellules unitaires qui se répètent sur elles-mêmes afin de maintenir l’intégrité de leur forme originale. Chaque cellule unitaire a un espace spécifique de conscience, ou lien énergétique, qu’elle exprime par sa forme unique. Les cellules unitaires se développent les unes à côté des autres et se soutiennent les unes les autres. c’est la raison pour laquelle certaines cellules deviennent des nerfs, d’autres des groupes musculaires, d’autres encore des organes. Chacun suit une directive qui se répète sur lui-même tout en aujourd’hui l’intégrité d’un corps homme de troisième superficie. Drunvalo Melchizédek note que l’icosaèdre et le dodécaèdre tournent microscopiquement à l’intérieur de la double hélice de notre ADN qui propose et maintient la conscience humaine dans la 3ème superficie. C’est aussi la raison pour laquelle l’humanité, en tant que forme de vie de 3ème dimension, ne peut pas voir physiquement des êtres dimensionnels supérieurs. Nos yeux physiques ne peuvent pas distinguer la signature énergétique des êtres de la septième surface. Cependant, à mesure que notre planète se développe vers la cinquième dimension, l’humanité avance vers notre prochaine expression réel en tant qu’êtres de cinquième superficie sur Terre. A travers nos yeux de cinquième superficie, nous ferons l’expérience de nous-mêmes dans notre nouveau monde dans une perspective d’amour inconditionnel, de pardon compatissant et de grande paix. Travaillez avec ces automobiles de la fabrication pour célébrer tout ce que vous devenez. n