My Library - Books





My mathematical library, and related matters thereof, as of 5 January 2018 (of an annual update), primarily of books and articles, but also of letters, pamphlets, reviews, patents, theses, puzzles, exhibition catalogues, conferences, videos, notes, reports, newspaper articles, reviews, interviews, obituaries and genealogy matters.


This is a personal collection of references with notes and annotations for my own mathematical researches especially as regards tessellations and Escher-like aspects, to which it is inclined, and that may come in useful for other researchers. Dates in bracket are of date of obtaining the publication. Occasionally a book is referenced that is not in my possession but is desirous of a mention for a variety of reasons, although this is made clear in the text. On occasions a book is refrenced that is way too advanced for me to be of any use, genrally from a bibligaphy. This is simply to have ‘seen and noted’ so I can rest easy that there is nothing that may otherwise have been of interest.


This was begun in 2006, and continues to the present day. Note that the text can be considered a perpetual work in progress, due to its very nature, of adatunal books and articles, and more, coming to light. The length and depth of each entry depends broadly on the significance of the book/article, albeit I am not always consistent in this desire. Not all entries have comments, due to time constraints. Occasional typos and omissions have simply to be accepted as the inevitable outcome of a work of such length and depth. Further, although I strive to be consistent, this is not always possible; I do indeed have other matters to attend!


A few clarifications to what may otherwise appear as obscure text:

1. Many references to the Cairo tiling can be seen, referring to my special interest in this tiling.

2. Some entries begin with ‘chance’ or ‘speculative purchase’. This refers to a book seen in a temporal sense, at a car boot sale or other such like sale, only available on that particular one-off occasion. Save for an obvious interest, typically for a book of possible interest, there is simply not the time to stand examining every page of a lengthy book for the topic of interest, and of which given that the price is usually inconsequential, a pound or under, and so rather than losing the opportunity, it is considered prudent to obtain the book, the sum involved being inconsequential, and can thus be written of if it proves of no use.





Abas, Syed Jan and Amer Shaker Salman. Symmetries of Islamic Geometrical Patterns. World Scientific 1995. (12 December 2009)

No Cairo.


Abbott, David (general editor). The Biographical Dictionary of Scientists. Mathematicians. Blond International 1985 (22 June 2003)


Abbott, P. Geometry. (Teach Yourself Books) The English Universities Press Ltd. 1962 First printed 1948 (19 July 1992) and Hodder and Stoughton. 1981 (26 July 1992)

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.


Abbott. Algebra (20 January 1987)


Abbott, P. and C. E. Kerridge. National Certificate Mathematics. Volumes 1 and 2 Technical College Series. The English Universities Press Ltd 1961 (19 July 1992, 26 July 1992, 21 June 1992)

Textbook, somewhat advanced. Of no practical use


Aczel, Amir D. Fermat’s Last Theorem. Unlocking the Secret of an Ancient Mathematical Problem. Penguin Books 1997 (16 July 2007)

Popular account of a historical quest; many digressions and good yarns.


Adams, D. M. Inorganic Solids: Introduction to Concepts in Solid-state Structural Chemistry.

Wiley-Blackwell, 1974. (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.


Adler, Irving. Mathematics. The Story of Numbers, Symbols and Space. 1958. Juvenile. (3 September 1995)


————. Groups in the New Mathematics. Dobson Books Ltd. 1968 (21 February 1998).

Of limited interest.


Agostini. Franco. Visual Games. Guild Publishing by arrangement with Macdonald & Co 1988. (5 February 1994)

Minor Escher text pp. 80-81, Waterfall, Sky and Water I pictures. Bizarrely, the Sky and Water I print is asymmetrically cropped!


————. Mathematical and Logical Games. Macdonald (sic) & Co. 1983 (27 July 1992).

Escher’s Ascending and Descending, p. 34, Mobius Strip II, p. 74, no text, just captions.


Ahrens, W. Mathematische Unterhaltungen und Spiele [Mathematical Recreations and Games], Leipzig 1901 (Downloaded from Internet archive 21 April 2015)

From a reference in Bradley (and MacMahon). General maths recreations, in the style of Rouse Ball. Like Rouse Ball, very little on tiling, barely worth mentioning. 424 pages.


Ainsley, Robert. Bluff your way in Maths. Ravette Limited 1988. (9 June 2002)


Albarn, Keith and Jenny Miall Smith. Diagram. The Instrument of Thought. Thames and Hudson, 1977 (26 July 2015)

Mystic nonsense throughout, in the ‘best’ tradition of Keith Critchlow. Unreadable save for skimming each page. A favourite ruse here is to quote well-known scientist/mathematicians to give the book a perceived creditability. Minor aspects of tessellation, within ‘perception’, pp,40, 43 and Islamic design, pp. 66-67.


Anderson, Paul and Deborah Curry. Imagined Worlds. Stories of Scientific Discovery. Ariel Books British Broadcasting Corporation, 1985. (28 August 1996, but seen much earlier, in April 1989)

Various essays on scientific discovery by eminent scientists, including Roger Penrose. of general interest overall, with a tiling aspect of Chapter 9 (by Deborah Curry), Beyond Space-Time, pp. 161-180, on Penrose, with a small tiling interest; Penrose chickens p. 177, and Escher's print Waterfall, p. 179, along with a popular discussion of Penrose tiles.


Angel, Henry. Plane and Solid Geometry. William Collins, Sons & Co., Limited 1885 (21 June 1992)

Typical geometry book of the day. Begins simply, from first principles, and then discusses more technical matters. The only tiling is on p. 26, a problem in copying a given tiling (square and octagon). I seem to have collected many instances of this ‘type’ in the early 1990s; any one really suffices for my needs.


Anon. Bricks and Concrete. By (author) the editors of Time-Life Books. 1984. First saw 21 December 1987, Scartho library

Although not a book on mathematics, including on this listing as it has brick tilings, p. 76, of which I briefly studied (a single sheet), with proto Escher-like additions,  on 21, 23 December 1987 and 5 January. As such, inconsequential.


Anonymous. Magic Snake Shapes. Corgi 1981 (14 July 1991)


Anonymous. Technical Drawing. Letts (22 March 1987)

From a reference of early maths studies, of 1986-1987.


Anonymous. Letts O Level Geometry (23 March 1987)

From a reference of early maths studies, of 1986-1987.


Anonymous. The New Mathematics

From a reference of early maths studies, of 1986-1987 (17 December 1986).


Anonymous. Longman Maths 1 (13, 18 February 1986) and 2 (12 February 1987)

From a reference of early maths studies, of 1986-1987


Anonymous. Maths to 16 (1 January 1987) by Bennet?


Anonymous. Practical Plane and Solid Geometry


————. The Sociable or One Thousand and One More Amusements. 1858 New York, Dick & Fitzgerald (Downloaded from Internet 10 June 2014). 375 pages

From Stegmann’s site. Best describes a series of ‘parlour games’, such as acting and magic tricks, popular of the day. Mathematically light with two small chapter on mathematical games: Fireside Games for Winter Amusements pp 274-84, Puzzles and Curious Paradoxes 286-300. Answers to Puzzles and Paradoxes 301-318. These contain loose geometric dissections, but nothing of particular note.


————. Tricks Played on Hand and Eye’ The UNESCO Courier, Vol., 19, no, 5 (1966), p. 14. (Note the year commonly given, 1964 (Locher, Schattsneider), is incorrect, it is 1966, as given by all authors where this is quoted; all copying from one another, likely from ? Locher is correct)

Somewhat of a disappointment, no text of note, with only two of Escher's pictures used, Belvedere and Waterfall.


————. Mathemagic. Childcraft Volume 13. World Book Childcraft International, Inc. 1979 (21 February 2004)

Juvenile. Occasional polyhedra, no tessellation.


————. Oddities. In Words, Pictures and Figures. Reader’s Digest Association Limited 1975. (July 1996 and 20 August 2003? The year is semi-legible). Two copies

Small-format ‘booklet’ 48 pages. Escher prints and minor essay pp. 25-28: Belvedere, Waterfall, and Ascending and Descending

Also see a later companion booklet, of 1988.


————. Nuffield Mathematics Teaching Project. 1971. (22 August 2004)

A series of ‘work card’ packs: Area (contains the Cairo pentagon, without reference to Cairo), Similarity 1, Similarity 2, Number Patterns, Topology, Number Patterns.


————. The World of Shape & Number. 1970 Marshall Cavendish Learning System. (6 February 1994.

Advanced Juvenile.


————. Artfile Patterns. Phaidon Press Limited 1990 (14 May 2005).

Patterns only, no text. Occasional tessellations


————. The Alhambra and the Generalife. (11 July 2004)

Looks like tour guide book (I also have another, different book of the same title) no date given, perhaps page torn out…


————. Mathematics in Primary Schools. Schools Council Curriculum Bulletin No. 1. HMSO Tilings p. 55, one diagram of octagons of interest.


————. Visual Elements 3. Marks and Patterns Clip Art. Columbus Books c 1989. (2 April 1994)

Strictly a pattern book, rather than mathematics. Book 3 of 10 in a series of a ‘visual elements’ premise. As such, of very little interest; tiling is of no substance, it being subsumed amongst general wall paper type patterns.


————. Visual Illusions. Reader’s Digest 1988. (20 August 2003? The year is semi-legible)

Small footprint booklet, 48 pages. Escher pp. 20-31, Day and Night. Broadly a retelling of existing illusions. Also see a later companion booklet, of 1975.


Apsley, Brenda (Devised by). Coloring Patterns: Fun Patterns. World International Publishing Limited. 1993 (1 April 1993).

Juvenile. Also see an accompanying book, of the same nature. A child’s colouring book, almost of a five-year-old level! Looking at both books again, I am at a loss as to why I obtained these, and furthermore at full price! The diagrams are as intended for their audience, of no challenge. That said there is the occasional diagram (tessellation) of interest - see p. 29 here, and p. 20 of Picture Patterns below. I can only think that I thought I had not seen these tilings, and so may as well have these books at a relatively low price.


————. (Devised by). Coloring Patterns: Picture Patterns. World International Publishing Limited. 1993 (1 April 1993).

See above.


Armstrong, Tim. Make Moving Patterns. How to Make Optical Illusions of Your Own. Tarquin Publications. 1982 (16 February 1991 (used) and 18 February 2007 (intact)


————. Colour Perception. A Practical Approach to Colour Theory. Tarquin Publications 1991 (30 April 1994)

Not strictly mathematical, but has the occasional crossover.


? Harpe P. De La. Quelques Problèmes Non Résolus en Géométrie Plane. L’Enseignement Mathématique, t 35 (1989), p. 227-243 (in French)

Cairo tiling page 232, likely taken from George Martin’s work, given that it is the same ‘unusual’ configuration.

c. late 2011?


Arnold, Arnold. Winners…and Other Losers in War and Peace. Paladin Grafton Books. 1989 (12 March 1999)


Arnold, George and Frank Cahill. The Magician’s Own Book or The Whole Art of Conjuring. 1862. New York, Dick & Fitzgerald, 18 Anne Street, London (Downloaded from Internet 18 June 2014)

As recommended on Rob Stegmann’s site, although indeed on magic, has much recreational mathematics; especially see sections on geometric aspects: ‘Curious Tricks in Geometry’ pp. 256-266, ‘Curious and Amusing Puzzles’, 266-290.


Ashcroft, Mike. Mathematics GCSE Passbook .1988. (15 October 1995)

Tessellations p. 130, barely worth the mention. Textbook.


Augarde, Tony. The Oxford Guide to Word Games. Oxford University Press 1984. (26 May 1996)

Not strictly mathematical, but related in a sense, with word play. 26 chapters



Bachet, de Mesiriac. Problemes plaisans et delectables qui se font par les nombres. 1612. A. Labosne Paris 1884 (downloaded from internet 5 May 2015)
From reference in MacMahon. As this title suggests, this is wholly on numbers; no tiling whatsoever.

Bain, Iain. Celtic Knotwork. Constable London 1991. (3 June 1993)

Baker, Lyndon et al. The Art Machine Pattern Book. Leapfrogs Ltd. 1990.


Ball, Johnny. Think of a Number. British Broadcasting Corporation 1979. (16 February 1995) (Soap bubbles p. 59)


————. Wonders Beyond Numbers. A Brief History of all Things Mathematical. Bloomsbury Sigma, 2017, Grimsby Library (7 October 2017)

Popular account. Has many interesting titbits, some new  to me. However, the length of the book (480 pages) mitigates against a considered reading, and so some pages were merely skimmed. some pages of interest include the Golden Ratio, pp. 50-51, where he gives, for me a new explanation.  Kepler pp. 306-314 plate in Hamonice Mundi  p. 313, Tessellation,  pp. 457-458, albeit a lightweight treatment. Escher, pp. 428-429, again lightweight. Pavement and Alhambra tilings on colour plate. Ideally requires a more leisurely read once more.


Ball, Phillip. Designing the Molecular World. Chemistry at the Frontier. Princeton University Press 1994 (19 February 1998).

Chapter 4, pages 111-141 has much on Quasicrystals and Penrose tiling. Escher’s page and minor text 128-129.


Ball, W. W. Rouse and Coxeter, H. S. M. Mathematical Recreations and Essays. (thirteenth edition). Dover Publications, Inc.1987. (30 April 1994)

Surprisingly light on tessellation, 105-107 only.


Banchoff, Thomas F. Beyond The Third Dimension. Geometry, Computer Graphics, and Higher Dimensions. (Distributed) W. H. Freeman and Company 1990. (30 April 1994)

A little hard to describe, the book consist of advanced concepts in geometry at a largely popular level, profusely illustrated. Loosely stated it is of dimensions higher or lower than three. No tessellation.


Barber, Frederick, et al. ‘Tiling the Plane’. Faculty Advancement in Mathematics Module, Lexington, Mass., 1989 LOOK FOR. (Reference in Comap)


Barnard, D. St P. Figure it Out. Pan Books Ltd 1973 (20 September 1992).



Barr, Stephen. Experiments in Topology. John Murray, London. 1965 (9 July 1994)


Barratt, Krome. Logic & Design in Art, Science and Mathematics. The Herbert Press 1989. First edition 1980. (24 April 2016)

First saw, and studied, in 1993, at Grimsby art school library. Decided to actively obtain subsequently (2016) upon a desire to review the study I had previously done. Upon receiving, my memory of the book had dimmed. I’m not quite sure what to make of it. I’m not too sure of Barrett’s, a designer, maths knowledge; It appears to be a compilation from other sources, with next to nothing of originality. The book drifts, in that one topic is introduced, before yet another, and another…. In short, it is too ambitious in scope; there is nothing is in depth or substance. The bibliography is at least extensive. Only minor tiling matters, of no consequence 47, 53, 66-67, 70-71, 196-197. It has other minor aspects of interest. As such, I have no plans to ‘study’ this once more.


Barrow, John D. Pi in the Sky. Counting, Thinking and Being. Penguin Books 1992 (22 July 2001).

Of limited interest; mostly philosophical musings.


————. The Infinite Book. Vintage 2005 (24 January 2015)

Has brief tiling matters, with of significance the Cairo tiling p. 16, although without attribution, and Penrose tiles. Also has minor reference to Escher, pp.130-131, with his print Sphere Spirals, referring to loxodromes.


Beard, R. S. (Colonel) Patterns in Space. Creative Publications Inc. 1973.

On geometry aspects, of nine chapters: Polygons, Tessellated Polygons, Polyhedra Patterns, Golden Section, Fibonacci numbers and related Drawings, Conics and Curves, Spirals, Triangle relationships, Primitive Triangles, Miscellaneous. A lot of formulae given, although the premise is of a diagram led book. Despite a chapter on ‘Tesselated Polygons, 23-42, not really concerning tessellations per se, but more of ‘patches’, and in general geometric constructions. The work on tessellations is taken from, or was inspired by. Beard’s article in Scripta Mathematicae, of the same title, which is reprinted in the book. Much of the formulae are too complicated for me, but nonetheless the diagrams are largely accessible. However, the book largely flatters to deceive.


Beer, Arthur and Peter Beer (editors). Vistas in Astronomy. Four Hundred Years Proceedings of Conferences held in honour of Johannes Kepler. Vol.18. Pergamon Press. 1975. (c. 2001)

A major collection of articles (of 1034 pages!) arising from the conference. Perhaps somewhat surprisingly tessellations, and to an extent polyhedra, are not really discussed. Instead, this is really more of his astronomical work. Chapter 11 is described as ‘Kepler as Mathematician and Physicist’. Of most interest here is Coxeter’s essay ‘Kepler and Mathematics’ pp. 661-670. Also see Chapter 14, pp. 861-876 ‘Kepler’s Crystallographic Ideas and his Tract ‘The Six–Cornered Snowflake’ by I. I. Shafranovskii, which touches on circle packing, and is illustrated.


Begelman, Mitchell and Martin Rees. Gravity's Fatal Attraction: Black Holes in the Universe

Cambridge University Press (Google Books, 16 June 2015)

Use of Escher's Circle Limit, Angels and Devils pp. 80-81. (**)


Bekkering, Betsy and Geert Bekkering. Stukje Voor Stukje: Geschiedenis van de Legpuzzel in Nederland. 1988 (In Dutch) Translated: Piece by Piece: A History of the Jigsaw Puzzle in the Netherlands (20 March 2016) Translation Printed 27 January 2017

Obtained in regards of interests in cluster puzzles, albeit with Bekkering telling me in a mail of 2014 that there is nothing there in this field. Has detail on background of Simplex pp.  57-58, and also on p. 30. Although there is nothing here on cluster puzzles per se, nonetheless it is of interest for background details of Dutch puzzle history.


Bekkering, Geert. Spaß und Geduld: zur Geschichte des Puzzlespiels in Deutschland. (In German). Translated: Fun and patience: the history of the puzzle in Germany. Husum. 2004 (20 March 2016) Translation Printed 27 January 2017

Obtained in regards of interests in cluster puzzles, with a Bekkering connection. Again, as above, there is nothing of direct interest. However, there is indeed peripheral interest, of what I surmised may occur, hence the speculative purchase. P. 56 has Heye Profi puzzle, which uses an adaptation of Escher's running man tessellation (without due credit), and of which upon further investigation can be seem to have been applied to numerous other puzzles by the company. Pp. 56-57 give a history of the company. Pp. 66, 68, 90, 92 are interesting in that they show a ‘wavy square’ tessellation cut, of 1914.


Bell, E. T. Mathematics Queen and Servant of Science. G. Bell & Sons Ltd. 1966 (24 October 1996 or 1998)


Bell, Marc. Marc Bell Presents the Magical World of M. C. Escher. Boca Raton Museum of Art January 20–April 11, 2010 (15 December 2014)

Nominally a catalogue of a Escher exhibition at the Boca Raton Museum of Art museum, although of the nature of a book. Has many unpublished drawings taken from microfiche. With essays by Salvatore Iaquinta (‘The Reluctant Pop Culture Phenom’ (sic), ‘Escher Memories: How Italy Shaped the Future’ and ‘Compass Card’), Federico Guidiceandrea (‘Filling The Void’) and Willem F. Veldhuysen (‘The Magical Work of M.C. Escher’). That by Iaquinta on the ‘Compass Card’ print is interesting, although whether his observations/conjectures is indeed correct needs confirmation.


Bell, R. C. Discovering Old Board Games. Shire Publications Ltd 1980 (18 February 2007)

Small format paperback.


————. The Boardgame Book. Marshall Cavendish Books First printing 1979, second printing 1983. (26 June 2016)

Oversize. A sumptuous presentation, and widely quoted as the bible of board games. although board games are not a matter of undue concern, I do indeed I have a passing interest, and about half of these are surprisingly new. Nothing particularly of a mathematical nature, although of course there is no reason to be so!


Bellos, Alex. Alex’s Adventures in Numberland. Dispatches from the Wonderful World of Mathematics. 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.


Belur, Ashwin; Blair Whitaker. A Practical Solution to Rubik’s Magic. Corgi Books 1986 (two copies, 27 September 1992 and 5 February 1994)


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 tiltle insinuets. Much of interest, although detailing this is not the most straight forward task. No tiling. (False) references are made to the golden ratio appearing in paintings, pp. 94-97, of which Mario Livio in The Golden Ratio p. 164 rebuts. For instance, it’s just ludicrous the figure of St Jerome.

This is a paperback, also see hardback in possession.


Beyer, Jinny. Designing Tessellations: The Secrets of Interlocking Patterns. Contemporary Books 1999 (11 December 2007)

Written by a patchwork designer. Mostly of compiling ‘pure’ tessellations, with a digression to the Escher aspect,  Chapter 10, the latter of which is a veritable disaster. Anyone who can be proud of ‘houses’, pp.206 and 222 reveals her lack of understanding of thre issues However, the pure tilings are better. 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, 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 all.


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


Billings, Robert Williams. The 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 another 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.


Birtwistle, Claude. Mathematical Puzzles and Perplexities: How to Make the Most of Them

Allen & Unwin, 1971. First saw c. 23 July 1987. Not in possession

A book that was briefly studied in 1987, but is of no consequence. Unavailable, save for a mad price, £180!


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 invidious.


Bourgoin, J. Arabic Geometrical Pattern & Design. Dover Publications, Inc.1973. (9 April 1993)

No Cairo.


Boles, Martha and Newman, Rochelle. Universal Patterns. Book 1. Pythagorean Press 1992 (19 November 1994).

The first of a * book series. It’s 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. Despite the title, it’s not a book on tiling.


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, pages 130-169, and other tiling instances scattered throughout the book.


Bolt, A. E. Machines, Mechanisms and Mathematics. Mathematics for the Majority. Chatto & Windus 1971 (22 August 2004)

Also see Murray T. and M Rust, for another in this series.


Bolt, Brian. The Amazing Mathematical Amusement Arcade. Cambridge University Press 1987 (9 June 2002)



————. Mathematical Activities. A resource book for teachers. Cambridge University Press 1987 (18 July 2009).

154 activities, of a recreational nature, pitched at a middle school level, with answers. Especially see Activities 39 Tessellations, page 28 and Activity 40, Tessellations and art, p.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)


Boyer, Carl B. A History of Mathematics. (Second edition, revised by Uta C. Merzbach) John Wiley & Sons Inc. 1991 (25 April 1998)


Boys, C. V. Soap Bubbles Their colours and forces which mold them. Dover Publications Inc. (19** reprint of 1959 edition) (18 October 1995)


Bradley, Amos Day. The 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 intesrest. 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, Giles. The Big Book of Puzzles and Games. Treasure Press. (First Published in Great Britain as four separate titles by Carousel Books) 1989. (Day not stated, July 1999)


————. The Big Book of Optical Illusions. Carousel Books 1980 (7 September 1997). Juvenile. Standard fare.

Not a ‘big book’ at all; standard paperback size!


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.


Briggs, William. Second Stage Mathematics. The Organised Science Series. University Correspondence College Press. 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.


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. With 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. Dale 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. As 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. No tessellation.


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)

Tilings occasionally discussed, Alhambra, Chapter 5, The Music of the Spheres pp. 155-188.


Brückner, Max. Vielecke und Vielfläche: Theorie und Gesschichte. (Translated: Polygons and Polyhedra) Leipzig: B. G. Teubner, 1900 (Downloaded from Internet archive 10 April 2015)

Frequently quoted in tiling concerns, such as by Schattsneider. 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 Schattsneider’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. Upon 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 The Ambidextrous Universe, of which in the preface Bunch defers to.


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, guess 2000)


Burrett, Anthony. Mathematics in Time and Space. Peter Haddock Ltd. 1973. Project Club Booklet (25 January 1997)

Mostly about time per se. Tilings pp. 48-49.




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 2015)

From a reference in Grünbaum. As such, this is very much like any other book on the Alhambra of the day; you 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.

Cantor, Moritz. 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, Louth library

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.

As 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 commentary.

Inevitably, 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 Size, 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 Press. 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 hexagon; none.


Clegg, Brian. A Brief History of Infinity. The Quest to Think the Unthinkable. Robinson, 2003 (6 May 2015)

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 passing.


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 I 137, Balcony 313.


Coffin, Stewart T. The Puzzling World of Polyhedral Dissections. Oxford University Press 1991. (3 June 1993)

Delightful throughout. Also, two-dimensional puzzles and dissections are briefly discussed, Chapters 1 and 2.


Cohen, Jack; Stewart, Ian. The Collapse of Chaos. Penguin Books 2000 (12 May 2002). Somewhat advanced.


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 Patterns. London: A&C Black 2003.


Conway, J. H. On Numbers and Games. Academic Press Inc. (London) Ltd. 1976 (14 September 1996)

Of limited interest, mostly advanced maths.


Conway, J. H. et al. The Symmetries of Things. A. K. Peters Ltd 2008 (19 March 2010).

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. The 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, p. 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. One 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. The Cambridge Guide 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)


————. 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! Many 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)

Escher pp. 57 (Horseman E67) - 59 (Beetles E91), 63. Very brief text.


Coxeter, H. 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 possession)

A minor study, in which the crystal studies are shared with other books of a like nature


Crane, Walter. The 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 significance.


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.


————. Islamic Patterns. An Analytical and Cosmological Approach. Thames and Hudson. Reprinted 2004. First paperback edition 1983. (17 May 2013) Kaplan gives a 1976 edition

Somewhat quirky; Islamic patterns interspersed with nonsensical cosmological and philosophical speculations thereof.


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.


Crowell, Robert A. Intersight One. State University of New York at Buffalo 1990. 10. Students' work from the Basic Design Studios of William S. Huff 80-85. (8 May 2003)

Parquet deformations. 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. Also 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 Percy Rollett)





Daintith, John and R. D. Nelson. (editors). The Penguin Dictionary of Mathematics. 1989 (4 November 2000)


Lord, Nick. ‘Constructing the 15th pentagon that tiles the plane’. Mathematical Gazette


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 pages, 49, 57, 60, 88-89, 103, 137, 252-253

Paving stone with overlapping circle tessellation, of c. 700 BC, page 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 the book.


————. Textbooks of ornamental design. The Application of Ornament. B. T. Batsford 1898 (20 May 2016, seen previously) PDF
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, the Art Journal and the 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 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 Ltd 1983

Although 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 Life 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; Howard Armstrong. The Youth Games Book. Resource Centre, Glasgow. 1985 (12 July 1998)

Intermediate Treatment Juvenile.


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, 158-160, 278-286. Juvenile


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)

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, 2002, 4th edition, 2009  (15 December 2017 edition 2002)

A little lightweight, of just 64 pages.


Devi, Shakuntala. Figuring. The Joy of Numbers. Andre Deutsch 1977 (18 October 1992)

On ‘elementary’ number calculations, and how she achieved such feats of stupendous calculation.


Dixon, Robert. Mathographics. Dover Publications 1991 (10 August 2006)


Dolan, Daniel T. and James Wilkinson. Teaching Problem Solving Strategies (7 May 1998, Hull)

A partial PC of a library book. A few pages on polyominoes, nothing of any significance or substance.


Donovan, Johnston 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 1914-1918….’

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) More Puzzles and Curious Problems. More than 250 tantalising brain teasers by the puzzle king. Collins Fontana Books. Small format paperback. (19 July 1992)

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 investigating.


————. (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.

No 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.




Eastaway, R. Enigmas. The World’s Most Puzzling Book. Arlington Books 1982. (31 October 1993)



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, Graphs, and 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 1995)

Although of repeat patterns and symmetry there is nothing of any real interest.


Elffers, Joost. Tangram. The Ancient Chinese Shape Game. Penguin books 1984. (19 May 1995)


Elffers, Joost; Schuyt, Michael.Tangram. The Ancient Chinese Shape Game. Barnes & Noble Books 2001 (26 April 2010).

A boxed set of tangrams and book.


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). Occasional 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!


————. Adventures with Impossible Figures. Tarquin Publications 1986. (9 April 1993)

Popular account.


————. 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. More of impossible objects, Ernst’s forte, rather than a generic optical illusion book. Has a scholarly bibliography. Escher prints Concave and Convex pp. 27, Belvedere 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. In 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 editions.


Escher, M. C. The Graphic Work of M. C. Escher. Oldbourne, London 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 of  which shows little new insight.


————. M. C. Escher 29 Master Prints. Harry N. Abrams, Inc. Publishers New York 1983 (9 April 1993)

Large format book. In addition to the 29 prints, both tessellation and others, the book includes an essay by Escher, 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 book.


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. The 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, Grimsby library

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 York 1961.


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 of 1987.


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. The 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 September 2012)

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 tessellation.


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).


Fetter, Nancy, 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 Gardner’s 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 The 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


Field, Robert. 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 pentagon.


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. The 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 Mathematical 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. English 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 Het oneindige

Small format paperback. A series of translated essays of Escher's own writings and previously unpublished speeches in Dutch, and so warmly welcomed. These include:

1. Newsletter of the Dutch Circle of Graphic Artists and Illustrators, No. 5, December, 1950. The Craft. 10-12. Dear Oey…

2. Newsletter of the Dutch Circle of Graphic Artists and Illustrators, No. 3, June, 1950. Our Brother 13-15. Dear Oey…

3. De Grafische (The Graphic Arts), No. 13, September, 1951. White-Grey-Black 16-18

4. Acceptance Speech by M. C. Escher upon receiving the Culture Prize of the City of Hilversum on March 5, 1965 19-22

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 2009)

Oversize. The premise is of a ‘grand picture book’ per se, with 74 works, of prints (mostly) and drawings. There 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 turns.

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.

Fourrey, 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 number 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)

Purchased 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 to.

My brief studies of this, of just four sheets, are dated 23 November and 2 December 1987, of  p. 96. Pages of interest include,  frontispiece, of a dragon space-filing curve, p.18, 30, of a metamorphosis, of  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 August 1991)
Usual repeated fare.

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 such.


Frederickson, Greg N. Dissections: Plane & Fancy. Cambridge University Press 1997. (28 February 1998)

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.

For 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 and Piano 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 Tessellations: 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’).


————. ‘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 1995)


French, P. Introducing Polyhedra. McGraw-Hill Publishing Company Limited. 1966 (24 October 1998).

Juvenile, Junior.


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 and 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 as useless 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. Escher.

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 Escher.

Therefore, it wasn’t a ‘special interest’ after all, but rather just a passing interest! But at least I know now.


Fuller, Buckminster R. Utopia or Oblivion. Penguin Books 1972 (20 September 1992).

Chapter 3 only of direct interest.



Gale, Howard et al. The Times Tournament of the Mind. Times Books Limited 1988. (not dated, c 10 years +)


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 interst, primarily of tiling matters, although drawing hard and fast lines is an invdious task at times. Quite simply his collection is indispensable! However, annoyinlg, and infurtaingly, these do not always refect the original title and so correlating like articles is not a straighforward 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 Scientific American (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 Further Reading


————. 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 Reading

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 October 2012)

(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. The 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 The Magic Numbers of Dr. Matrix) Charles Scribner’s and Sons, 1976 (7 November 2012)

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 expeting other articles with the Dr Matrix coloums, as with other books in which an initial  title is insinuated. I have the second edition, The Incredible Dr. Matrix.


————. 5. The Unexpected Hanging and Other Mathematical Diversions. (1969; UK Further Mathematical Diversions) Simon and Shuster 1969 (14 June 2011)

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, Bibliography

Of most interest: Geometric Dissections, pp. 43-51 and Rep-tiles Replicating Figures on the Plane, pp. 222-233


————. 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. Mathematical 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)

1 Optical 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 2013)

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, 13 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 contains extended Cairo references p.176, and includes a little extra to the text per se , with It underlies… p. 171 (the original article in Scientific American 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 from.

Also 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 The 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 Omega

6 is on MacMahon and his cube puzzles.


————. 15. The Last Recreations. Copernicus An imprint of Springer-Verlag 1997 (26 March 2013)

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)


————. Puzzles from Other Worlds. Fantastical brainteasers from Isaac Asimov’s Science Fiction Magazine. Oxford University Press. 1989 (24 October 1998)


Gardner, Martin. Gardner’s Whys & Wherefores. Oxford University Press 1990 (5 October 1996).

Mostly philosophical 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)



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. However, 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, p. 167.


Gellart, W et al. The VNR Concise Encyclopedia of Mathematics. Van Nostrand Reinhold Company 1977 First saw c. 1986 (27 August 1997)

Principia-esque! 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. The 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 real interest.


Gibbons, Stanley. Stanley Gibbons Stamp Catalogue Part 4 Benelux. 5th edition, 2003. (7 December 2013)

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)

Occasional Escher illustrations; 55-?


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 hare 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 August 2017)

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 Grade. 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; Johnson, Donovan A. The Theorem of Pythagoras. Exploring Mathematics on Your Own 4. John Murray 1965 (22 October 2005)


————. Number Patterns Exploring Mathematics on Your Own 3. John Murray 1964 (24 October 2005)

Juvenile, advanced.


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 pp.150, 152.


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; not that I’ve done much with it!


Gombrich, E. H. 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, 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.


————. 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.


Gorini, Catherine A. The 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, Duncan; 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. The 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

Schattsneider 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’ ruse.



Grünbaum, B. and G. C. Shephard. Tilings and Patterns. W. H. Freeman and Company New York, 1987 (11 January 1993; first saw in 1989)

Indispensable! (although much is way too advanced for me) Largely, indeed overwhelmingly, academic, but still accessible on occasion. Cairo-esque p. 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.

Gullberg, 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.

Gunther, 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 Mathematics, 1984.

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 Rigby

Escheresch, Athelstan Spilhaus

Henry Ernest Dudeney: Britain’s Greatest Puzzlist, Angela Newing (has much detail on Dudeney not previously published)

The Utility of Recreational Mathematics, David Singmaster

Puzzles Old & New: Some historical Notes

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 1986)


Hand, William. ‘Scientific Mysticism’ in Rosicrucian Heritage No. 1 2005. (9 June 2015)

Use of Escher's print Print Gallery, p. 21; no other mention of Escher in article.


Hannas, Linda (Introduction). Two 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, written for the London exhibition of 1968, with much input by Hannas. A speculative purchase, being a 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, p. 37, albeit without a picture. However, disarmingly, two mistakes are made in the text, with ‘Miss’ rather than Mrs and ‘Clark’ rather than Clarke. Another 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 my 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.

As 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.

The site 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 2016)

Jigsaw puzzle interest. Although 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.


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? where Heesch shows his Set of 28, including the Wikipedia paving, no. 9. although not exact….. P. 68 shows the tile in detail.


Hendler, Muncie. 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.


Hemmings, Ray and Dick Tahta. Images of Infinity. Tarquin Publications 1992 (3 June 1993)

Escher’s Circle Limit I, p. 14.


Heritage, R. Learning Maths Book 1 (first saw 14 January 1988)

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.


Heyden Van der, A. The 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 discernable, 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. Modern 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 September 2017)

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. Upon 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!


Highland, 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.


Hilbert, 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’!


Hill, 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 10+ years).

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 2011)


————. 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 2005)

Tessellations pp. 242, 247, 253, 404-415. All inconsequential. 16-year-age.


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.


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’ life.


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, 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!


————. Metamagical 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 Olseon, 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. Pan Books Limited 1940, 1967 (7 March 1993 hardback; 16 April 1995 paperback)


————. Man Must Measure. The Wonderful World of Mathematics. Rathbone Books, London 1955 (4 August 1996)

Oversize, Juvenile.


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.


Hollands, Roy. A Dictionary of Mathematics. Longman 1980 (not date stamped, c.10+ years)

Tessellation p. 151, inconsequential.


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. The Second big book of puzzles. Puffin Books 1976 (12 September 1993).

Usual fare. The title is misleading; it’s a standard size paperback!


Holt, Michael. What is the New Maths? First published in 1967 by Anthony Blond Ltd. First saw c. 18 Sep 1986 (23 September 2000)

A small format hardback, of just 99 pages. 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).

(From a reference in Schattschneider and Locher). A small format paperback, of just 96 pages, 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 2015)
From a reference in MacMahon. No 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)

No tessellation.


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 & London 1978 (16 March 1996)


Huff, Darrell. How to Lie with Statistics. Penguin Books 1988. (11 July 1998)

Of limited interest.




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-popular, 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 p. 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.

Many 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 p. 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 inconvenient).

Full 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 worthless.

Jacoby, 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 geometrical nature.

Jackson, John. Rational amusements for winter evenings. 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.

Jackson, Tom (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. However, 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. Modern School Mathematics Books 1-4. Oxford University Press,  1959 (First seen September 1987)

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 most likely.


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 books.


Jaworski, John & Stewart, Ian. Nut-crackers: Puzzles and Games to boggle the mind. Pan Books Ltd 1976 (14 October 2000)


Jeger, Max. Transformation Geometry. George Allen and Unwin Ltd. 1970 (date not stated)

Of limited interest.


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 Publications

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)

Popular account.


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. This 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).

Standard fare.


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-. The 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, Graphs, and 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)

First  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 additional references.

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.


Kasnar, Edward, Newman, James. Mathematics and the Imagination. G. Bell and Sons, Ltd. 1970 (25 April 1999)

Space-filling curves pp. 343-355.


Kay, Keith. Take A A Closer Look. Bright Intervals Books 1991 (3 June 1993)

On optical illusions. Escher tessellations Ascending and Descending, p. 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)

Advanced juvenile.


Kelsey, Kenneth; King, David. 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 and London. Second printing 1992.

As a broad statement, a series on perspective, of noatable substance. Much of interest and accessible. For example, 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. p. 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 between.


Kenney, Margaret J. and Stanley J. Bezuszka. Tessellations Using Logo

Dale Seymour Publications, 1987 (8 March 1995). From Jonathan Press.

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 consequence.


Kepes, Gyorgy (ed). Education 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 certain.

I have no plans to re-visit this book.


Kepler, Johannes. Harmony of the World.

Available on-line from


Kepler Johannes. The 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.


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 p. 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. The 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)

Although strictly 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.


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) Dudeneyesque in 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, 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; 75-79.


————. An Inventor in the Garden of Eden. Cambridge University Press 1994 (22 January 2007)

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.


Land, Frank. The Language of Mathematics. John Murray 1960 (21 June 1992)


Langdon, John. Wordplay. Bantam Press. 2005 (3 March 2007)

Delightful. Langdon can be desribed as a master of his craft. Escher pp. 170 Sky and Water I, 181 Angels and Devils.


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, Snape. A Way With Maths


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. The 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 Pavilons 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. 2011)

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. Curves. 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 by Leapfrogs.


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. Whether 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 Metamorphosis, Chapter 4, p. 138, Relativity; Chapter 5 p. 232, Reptiles.


Levy Joel? Optical 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.

Note 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 interest.

Leuvechon, Jean. Récréation Mathématique. no 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. The Snowflake Winter’s Secret Beauty. Colin Baxter Photography Ltd, 2004. First published 2003, US (22 May 2016)

Popular account, from a physicist.


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 pp91-99, 155 pages.


Liebeck, Pamela. How Children Learn Mathematics. Penguin Books 1988 (16 February 1995) Tessellation, 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 tile.


Livio, Mario. The 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. 203-206.

Note that the Livio here is not the same as a namesake, Livio Zuccha of tiling fame; it’s easy to mix them up.


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 1988 (9 April 1993) First saw 1987, under a different title The Infinite World of M. C. Escher. Apparently of 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.


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 stamped).

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. ‘Indirect’ Cairo reference p. 88. Escher p. 4, Shells and Starfish, E42, Fish E41, p. 66 Lizards, E56.


Lodding, Ken. Byte. The small systems journal. 1979 Volume 4 No. 2 (February) 21 September 2016)

‘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. Many 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 AustaliaPuzzle 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, p. 120 Running man, p.163 Fish, p. 164 Lizards, p. 166 Butterflies.


————. Concepts & Images 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. The 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 with foreknowledge, as the picture is from afar that without cognisance of the tiling would otherwise pass unnoticed. The 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 uncredited 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 2014)

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 sense.




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? (Moors 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 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 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 2001)

Essentially an illustrative book, with any text at a premium. Note that the 1001 designs are not discussed individually.


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. The 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. The Fractal Geometry of Nature. (updated and augmented) W. H. Freeman and Company, 1983? (10 October 2016. PDF.

A weighty tome of 468 pages. I have seen occasional reverences 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 pages.


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 desibeds this as of CSE level, which book I saw is uncertain. a refnce gives ‘No. 3’, but this may be association with a page number of the book to hand, not necessarily of Book 3


Marks, Robert W. The New Mathematics Dictionary and Handbook. 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 schools, 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  indeed 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. Although 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 tessellation.


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 website). Mostly of background matters as to the intricacies of paving; as such, there is next to nothing on pattern in the broad sense. Of little to no interest mathematically.


McGary, Debi. Wonderful Wood Puzzles. Plaid Enterprises Inc, Norcross, GA 1996


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. The 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. 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. The 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. Optical 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.


Midonick, Henrietta. The Treasury of Mathematics: 2. Penguin Books 1965 (29 October 2005) 24 Biographies.


Miller, Charles D., Vern E Heeren, John E. Hornsby, Jr. Mathematical 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 1997)

‘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 November 2017)

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. So lightweight as be barely worth comment.


Mold, Josephine. Circles. Topics From Mathematics. Cambridge University Press 1967. (20 August 2000?)

Small, 32-page booklet. Very accessible, with much of interest.


————. Topics From Mathematics. Tessellations. 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 du 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.


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 2007)

Escher’s Relativity p. 55, with minor text barely worth the mention.


Morgan, Bryan. Men and Discoveries in Mathematics. John Murray 1972 (24 October 1998)


Morgan, W; Pickering, J. R. Mathematics I and 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 Husband. 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. 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. 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. No tessellation as such, although plenty of off-shoots.


————. Leonardo’s 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. The 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 Square & 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 button’ myth.


————. 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, 1901-1902’.

Historically significant, as here are the first true life-like Escher tessellations (I do not consider the ‘Peru’ types bona fide). 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), p.53 (woman), p.57 (woman, with gaps). Birds of p. 25 is noticeably favoured for true premise and inherent quality.


Mottershead, 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.

The cover has a op art design apparently attributed to one Chris Belson. However, 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 p. 64 on see p. 128 of Sources…’ without any mention of Gettings!

The first of two book of a like nature by Mottershead, although wide apart in chronology, 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 in1987 (at Grimsby reference library).


Mott-Smith, Geoffrey. The Handy Book of Indoor Games. Permabooks. 1949. Mostly card games. (c. 1997)


Munari, Bruno. Design as Art. Penguin Books Ltd 1971 (Not date stamped, c 2006, at a guess)

Design, rather than maths. Occasional mathematics. Note that Munari is an associate of Mari.


Murphy, Lawrence R. The 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 format type.


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 design. Cairo tiling, unatributed, 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)




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 convenenience (although the book is economically available). Nasr is a prolific author, with 29 publications to his name (on the internet archive site), easly 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.

Of note in the context of Escher cover art is a snippet of Escher’s plane tiling of Swans on the cover (shared with another, unrelated picture).


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. The World of Mathematics – Volumes 1-4 Simon & Schuster
2480pp. (4 Volumes) (September 2016, pdf)


————. The Universal Encyclopedia of Mathematics. Pan Books 1976 (1 April 1993)


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 tessellation.


Nichols, T. B. and Norman Keep. Geometry of Construction. Cleaver-Hume Press Ltd 1959. First published 1947. First saw 1987 (27 August 2000)

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.


Nixon, J. T. World of Shapes. Oliver and Boyd Ltd. 1968 (5 October 1998)



Northrop, Eugene P. Riddles in Mathematics. The English Universities Press Ltd. 1945 and also Penguin Books 1975. (16 November 1996 and 17 October 1998)

Largely of paradoxes and fallacies, derived from stated sources, as detailed in the preface. Not tessellation as such, but of much related material; of minor optical illusions, dissections, and space filling curves, to name but few. The overall tenure is largely of an academic nature, although the above is indeed of a popular level.


Nunn, G. Modern Mathematics. Macdonald And Evans. 1978 First saw c. 31 July 1987 (22 December 2016)

Small format paperback. As 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. there is no Escher-like element whatsoever. However, some most rudimentary Escher-like tesselations can be found on in the Appendix, p. 327, which is ‘typical teacher’ i.e. no idea!





O’Beirne, T. H. Puzzles & Paradoxes. Oxford University Press, 1965 (17 February 2015)

A collection of articles which appeared in New Scientist from 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 (14 November 1998)


O’Daffer, Phares.G; Clemens, Stanley R. Geometry. An Investigative Approach 2nd edition Addison-Wesley Publishing Company 1992. (23 October 2010).

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).

Especially see: William Huff. ‘The Landscape Handscroll and the Parquet Deformation’, 307-314. This 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


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 20th Century Toys. Bracken Books 1996 (first printed 1995) (26 June 2016)


O’Shea, Donal. The Poincaré Conjecture. In Search of the Shape of the Universe. Allen Lane, 2007. (21 April 2012)

Semi-popular account.


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 1993)

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.


Paling, D. Elementary Maths. Details Pending

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. The Collector’s Guide To Cluster Puzzles Of The 1960s and 1970s. Self Published. 2003. (5 November 2013)

Essential reading. History of cluster puzzles (of the type as evinced by Escher’s Plane Tiling I and 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)


————. Mathematical Scandals. Wide World Publishing/Tetra first published 1997 3rd printing 1999 (31 August 2002)

A few good yarns, although no original research per se.


Paraquin, Charles H. Eye Teasers. Optical Illusion Puzzles. Granada Publishing Limited 1979 (19 July 1992).

Juvenile. Usual repeats of established illusions.


Parsons, Richard. GCSE Mathematics Intermediate Level. Coordination Group Publications1998. (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)

Small format paperback, of mild general interest, but nothing of note as regards my specific interests.


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)

As such, although largely on popular subjects, there is very little of direct interest to me here. Chapter 5, Two-Way Stretch, on topology, has elements of interest.


————. Geometry and The Liberal Arts. Penguin Books 1976 (14 July 2001)


Peitgen, Heinz-Otto et al. Fractals For The Classroom. Strategic Activities Volumes 1 and 2. Springer-Verlag 1991 and 1992 (6 August 1997)


Penkith, F. E. Confidence Mathematics. Macmillan Education Ltd. Reprinted 1990 (first edition 1985) (27 October 2001, Louth).

No tessellation. Basic 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 1994)

Mostly too advanced for me. Occasional tessellation, of non-periodic tilings, and their background, pp. 172-178. Occasional Escher references, Circle Limit I p. 203. Quasicrystals pp. 562-563.


————. Shadows of the Mind. Vintage 1995. (5 November 2011)

As to be expected by the tenure of the book, this is almost entirely beyond me, the only aspect of understandably is a short discussion on tiling 29-33, Robert Amman influenced.


————. 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 Publishers1985

Astronomia Recreativa Physics for Entertainment (1913) 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

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. 83-86.


Petrie, Flinders W. M. Egyptian Decorative Art. Arno Press. 1978. First published 1895 (19 November 1994, York)

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.


Pickover, Clifford. (24 July 2016)


Pinto, Edward & Eva R. Tunbridge and Scottish Woodware. G. Bell & Sons, 1970. c. summer 2016

Non-mathematical interest, 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.


Plichta, Peter. God’s Secret Formula. Discovering the riddle of the universe and the prime number code. Element 1997 (11 September 2000)


Pohl, Victoria. How to Enrich Geometry Using String Designs. National Council of Teachers of Mathematics. 1991 (30 April 1994)


Polster, Burkard (with foreword by John Langdon). Eye Twisters. Ambigrams & Other Visual Puzzles to Amaze and Entertain. Constable, London. 2007 (2010)

Prize in a tessellation contest 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 2011)

Gift of Jeffrey Price. Much of interest, with many previously unpublished materials and Price’s own insights concerning Escher.


Priestly, J. B. Man and Time. Aldus Books London 1964.


Pye, David. The Nature & Aesthetics of Design. Barry and Jenkins Ltd 1978 (18 October 2008)


Pythagoras (the entire archive). Mathematics journal in Dutch. Of interest:

No. 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 kleuren’, 22-23





Raba, Raoul. Zoo Mathématique. ACL Les Éditions Kangourou 1998 editor André Deledicq (In French) (14 March 2015)


Racinet, A. The Encyclopedia of Ornament. Studio Editions 1989. (Originally published as Polychromatic Ornament by Henry Sotheran and Co. London 1873) (10 August 1993)

Essentially of ornament rather than tessellations. Although of a 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 examination of the text. The two red and blue diagrams of Egyptian tilings, p. 77 are repeated in**.  p. 129 and 135 are Arabic patterns.


Raeburn, Michael. An Outline of World Architecture. First published 1973 Octopus Books Limited. (23 October 2015)

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 the general procedures 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 audience.


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 2001)

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 1994)



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 Numbers

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 examples throughout.


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 2016)

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 cover.


Reichmann, W.J. The Spell of Mathematics. Methuen & Co Ltd 1967 (14 July 2001).

Of limited interest. Too advanced.


Richardson, Margaret H. The Sign of the Motor Car. Dennis, Massachusetts, 1926, privately printed. REFERENCE NOT SEEN

‘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. 1997?)

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. This influenced my studies of the day when first seen, in December 1987.


Rogers, James T. The Story of Mathematics. Hodder and Stoughton 1979 (8 August 2004) History, 16-year-age range.


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 print Frontispiece and p. 25. Juvenile. This led to studies of p. 21 (not Escher-like), of three different periods, of August/October1987, 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.

Row, Sundara 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 elsewhere. 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)

Has Escher cover of Hand with Reflecting Sphere (Juvenile).


Rubin, Don. What’s the Big Idea? And 35 other unusual puzzles. J.B. Lippincott Company 1979. (9 July 1995)


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.


Rust, Murray- T. M. Mathematical Pattern. Mathematics for the Majority. Chatto & Windus 1971 (22 August 2004).

Pattern in the broader sense, rather than confined to tessellation. Also see A. E. Bolt for another book of this series.




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 which ‘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 1998)


Sackson, Sid. A Gamut of Games. Hutchinson & Co. Ltd. 1983. (27 August 1997)



Salvadori, Mario. The Art of Construction Projects and Principles for Beginning Engineers & Architects (25 October 2014) Chicago Review Press 1990, third edition

Occasional crossover to mathematics.


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 January 2013)

Although not a mathematics book per se, included as it has an Escher print, 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. (Second)


Sarhangi, Reza (Ed). Bridges. Mathematical Connections in Art, Music, and Science. Conference Proceedings 2000 (7 March 2006) South Western College, Kansas (Third)


Sarhangi, Reza (Ed). Bridges. Mathematical Connections in Art, Music, and Science. Conference Proceedings 2001 (7 March 2006) South Western College, Kansas (Fourth)


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. Mathematical Connections in Art, Music, and Science. Conference Proceedings 2004 (7 March 2006). South Western College, Kansas (Seventh)


Sarhangi, Reza; Moody, Robert V. (Ed). Renaissance Banff. Bridges. Mathematical Connections in Art, Music, and Science. Conference Proceedings 2005 (7 March 2006). Canada (Eighth)


Sarhangi, Reza; John Sharp (Eds). Bridges. Mathematical 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 known Cairo tessellation shown in Figure 1. Also, other minor references essentially in passing.


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. Dover Publications Inc 1954 (7 December 1994)


Sattin, Anthony and Sylvie Franquet. Explorer Egypt. AA Publishing. Reprinted 2000. First published 1996 (not seen). (18 May 2013)

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. An old fashioned ‘good yarn’, with complex mathematics discussed in simplified terms for the layman. Nice discussion on Simon Norton among others.


Sawyer, W.W. The Search for Pattern. Penguin Books 1970. (17 September 1994).

Not recreational maths.


Prelude to Mathematics. Penguin Books 1961. (9 July 1994).

Of limited interest. Better than his other book The Search for Pattern.


————. Vision in Elementary Mathematics. Penguin Books 1964 (2 April 1994)

Of limited interest.


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, p. 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 February 1991)

Revised edition 2004 (23 March 2010)



Schattschneider, Doris; Walker, W. M. C. Escher Kaleidocycles. Tarquin Publications 1982 (19 August 1988)

Cairo like tiling, page 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 1997)

Schubert, Hermann. Mathematische Mussestunden. Volumes I, II and III. Leipzig 1898. (Downloaded from internet 14 May 2015)
From a reference in MacMahon. In three volumes. Volume 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 Probelms112-126 (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. p. 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. Puzzles and Teasers. Faber and Faber. 1970 (24 October 1998) Dudeneyesque.


Sealey, L.G. W. The Shape of Things. Basil Blackwell Oxford 1967 (12 October 2002)

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. Boston 1880.


Seiter, Charles. Everyday Math for Dummies. Hungary Minds Inc. 1995 (17 April 2005)


Seitz, William C. The 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

The Responsive 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, among others.

Of note is painted tessellation by Equipo 57 (a Spanish collective), p. 23; Schröeder’s staircase p. 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 previously)

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. The 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 respectively. 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.


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. Dale Seymour Publications 1992 (10 August 2006)

Advanced Juvenile.


————. 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. The 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. In 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. 17.


————. 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’, p. 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 translation.


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.


Singh, Simon. Fermat’s Last Theorem. Fourth Estate, London 1998 (19 February 2007)


————. The Code Book. Fourth Estate, London 1999 (30 June 2013)

General interest.


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.


Slade, Richard. Geometrical Patterns. Faber and Faber Limited 1970. (24 October 1998) Contains interesting historical French curve source reference, page 16, different from others. 16-year-old audience.


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, p. 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


Smeltzer, Victoria; Smeltzer, Patricia. Mathematics Encyclopedia. Burke Books 1980 (18 February 2000?)

Juvenile, 10-year-old. Tessellation page 75. Hexagons, not worth mentioning.


Smith, Thyra. The Story of Measurement. Basil Blackwell Oxford. 1968. (12 October 2002). Juvenile.


————. The Story of Numbers. Basil Blackwell Oxford. 1969. (12 October 2002).



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 illusions.


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. This 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)  Hardback

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 are  neglected.

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 August 1994)

No tessellation (Hardback). P. 266 has a clown figure of a five-fold nature which I studied in 1989. Parabolas p. 149


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. Of 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)

No tessellation.


SMP Book H. Cambridge University Press 1972. (16 October 1993) Doncaster

Minor tessellation, pp. 83-84, with a P. Murphy chicken-like motif  p. 84, within a chapter on Geometry, pp. 76-90


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)

No tessellation.


SMP Book Z. Cambridge University Press 1974 (25 August 1991)

No tessellation.


SMP Teacher’s Guide for Book X. Cambridge University Press 1974 (25 August 1991)

No tessellation.


SMP Teacher’s Guide for Book C. Cambridge University Press 1971 (18 April 1993)

No tessellation.


SMP Book X. Cambridge University Press 1975 (not dated)

No tessellation.


SMP 11-16 R3. Cambridge University Press 1989 (14 August 1994)

Impossible objects 116-117 ‘Penrose-like’ stairs page 125. No tessellation.


Smullyan, Raymond M. What is the Name of this Book. The Riddle of Dracula and other Logical Puzzles. Prentice-Hall Inc. 1978 (date semi legible – 2000?)

Logic Puzzles.


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.

A later colour edition was subsequently seen in both Cleethorpes and Grimsby libraries.


Staněk, V. J. Beauty 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 central library)

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 October 2007)

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 Productions (19 March 2010)

Juvenile content, despite the serious title, of only 40 pages. Stephens apparently wrote the entire text, with 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.


————. 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. 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.


————. Concepts of Modern Mathematics. Penguin Books 1982 (16 May 1999) (17 November 1994 and 24 August 2004)

Of limited interest, somewhat technical.


————. Does God Play Dice? The 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)

Chance 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. No tessellation


————. Professor Stewart’s Cabinet of Mathematical Curiosities. Profile Books 2008 (4 June 2011)

Popular maths.


————. From Here to Infinity. A Guide to Today’s Mathematics. Oxford University Press 1996. (17 June 2012)

Popular account of hard to understand concepts.


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.


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. As 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.

There 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 p. 144. Reference to Arnold (Nol) Escher, p. 206 as regard mountain formation. p. 482 Quasicrystals.


Tammadge, Alan; Star, Phyllis. A Parents’ Guide to School Mathematics. Cambridge University Press 1977 (4 October 1997)


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 & Leanne Rylands. Cube Games. 92 Classic Games, Puzzles & Solutions. Penguin Books 1981. (20 June 1993)


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 nature.

As given by Andrew Crompton. Author unknown.


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’). As 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. On Growth and Form. Abridged edition by J. T. Bonner. Cambridge University Press. 1975 (13 July 2009)


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 1993)

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

For 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. Optical Illusions. Pergamon Press 1964. (26 July 1997)

A 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 succeeding chapters).


Townsend, Charles Barry. The 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

As 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 Townsend here.


Tufnell, Richard. Introducing Design and Communication. 1986 Nelson Thornes Ltd (c. 14 April 1987) SEEN.

Some minor tessellation studies, nothing in the way of originality.


Tyler, Tom. British Jigsaw Puzzles of the 20th Century. Richard Dennis 1997 (22 March 2014)

Of jigsaw puzzle interest. Although 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 note include:

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, 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! As such, I am more than a little under whelmed with such a brief references of no particular insight of just a single  sentence; perhaps 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 Puchiger.


Valette, G. Les Partages d’un Polygone Convexe en 4 Polygones Semblables au premier (in French)


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.


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 100th 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, 1998.

Tessellation 130-131, Polyhedron 152.


————. 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 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)

Simply a pattern book, with line drawings from various cultures around the world. Text is purposefully kept to a minimum at the beginning of the book. Has many interesting designs. No Cairo tiling.


————. 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 intest. Chapter specically 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, p. 87, with Waterfall and general text.


Walker, Michelle. The 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.

Interestingly in the bibliography, Walker quotes David Wade (2) and Johannes Itten, not to mention Jinny Beyer.


Walter, Marion. The Mirror Puzzle Book. Tarquin Publications, 1985 (30 January 1999)

Juvenile, of no interest.


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 Press. 1988 Second Printing 1992. (30 April 1994)

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, by Stephenson and Suddards, 1897, p. 18. 158 paving tiles from fourteenth century, France. p. 172, stylised swans from Escher, p. 206 arrowhead tiling variation, p. 219 Escher's lizards, p. 232 Chinese traditional design.


Wells, A. F. The Third Dimension in Chemistry. University Press, Oxford, 1956

Cairo tilings pp. 24-25, in the context of Laves tilings, although not named as such ( 8 February 2016). This is 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 Wells himself.


————. 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 N. 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 Models. Cambridge University Press 1989. (3 June 1993)

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)

N.B. Rubik’s puzzle.


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-. Mathematics. The Science History of the Universe. The Waverley Book Company 1911 (Date not stated)


Whistler, Rex and Laurence Whistler. AHA.  First published 1948 again 1978. John Murray (23 September 2017)

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. The images are by Rex, with accompanying verse by Laurence, his brother. Some are better than others.

Note 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.


————. Perspective. A Guide for Artists, Architects and Designers. 1982. Batsford Academic and Educational Ltd.

Recommended by 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.


Williams, Anne D. The 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.

Of 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 Williams.


————. 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 1993)

Cairo tiling page.


Willson, John. Mosaic and Tessellated Patterns. How to Create Them. Dover Publications, Inc. 1983. (30 April 1994)

Cairo tiling plate 3. (Neglected until 7 May 2013!)

Very pleasing indeed, with many simple, but interesting tilings, and ideas thereof.


Wilson, Eva. Islamic Designs. British Museum Press. First published 1988, Fourth Impression 1992 (3 June 1993)

The 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)

Popular account.


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. No 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. An 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 Dedicata


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. However, 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. Walker 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. 17.




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 August 2016)

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 include 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.