My mathematical library, and related matters thereof, as of 8 January 2019, of an continuous update, rather than yearly, as previously, primarily of books and articles, but also of letters, pamphlets, reviews, patents, theses, puzzles per se, jigsaw 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 referenced that is way too advanced for me to be of any use, generally
from a bibliography. A typical example would be from
This listing 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 additional 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. Some of the entries have additional biographical detail on the author, generally taken from Wikipedia. This is for the sake of general interest, when the author's background is not generally known. 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 ‘from a library sale’. Typically, with other would-be purchasers present, it is best to keep the book and examine in detail later in the sale, or later at home. Typically, the books are of a price that is inconsequential, often pennies, or no more than a pound. Such relatively small sums of money is thus inconsequential, and thereby offers up books of possible interest (in whatever subject) that perhaps I would not normally pay full or even half price for. The sum involved being inconsequential, and can thus be written of if it proves of no use. 3. 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. 4. Some references to jigsaw puzzles may seem otherwise obscure in a mathematical context, but what is a jigsaw puzzle if not a tessellation? Here however, these are with historical matters or mathematics of some kind underlying them. 5. Some entries have background detail as to the author, often taken from Wikipedia. This is typically where the author is perhaps less well known, and I desire to know a little of the background. On occasions, entries are discussed simply, for the sake of brevity, with a series of short stock phrases. The key: ‘Interested bystander’. Within my core interest in tessellation, even in my specialised field, there are aspects that although I am interested in, I do not undertake anything in the way of active study, generally of a popular level, such as with geometric dissections and polyominoes. Rather, I simply ‘stand back’ and observe and admire as an ‘interested bystander’ would, leaving the study to those of much greater ability than my low-level efforts.
‘Of peripheral interest’. Some references here are included despite on the face of it having nothing to do with tessellation. Some of these include such as pavements, where these are or can be said to be, only token references, or indeed strictly none at all. However, at all times, there does indeed remain some underlying tessellation interest, even if not obvious.
‘Seen and noted’. In the course of my studies, many books and articles contain references to additional works, some of a more obvious interest than others. However, not all of these are strictly relevant, some being at too advanced a level for my limited mathematical understanding. However, only by examining these can this matter typically be determined for certainty. This being so, such books and articles are simply stated as ‘seen and noted’, with the implication that these are of an advanced nature, of no use to me. Rather than leaving the matter open-ended, I can now ‘rest easy’ in the knowledge that the reference is superfluous to my needs. ‘Of pavement interest’. Typically, but not necessarily, of lesser mathematical interest. Broadly, this can be described as an off-shoot of tessellation, in which pavements, and by extension, roads, are studied. Such matters are thus likely of a lesser degree of interest to the typical reader here. These range from nothing on all on tessellation (such as pavement materials, history, techniques etc.) to considerable overlaps. However, within a broad tessellation interest, they nonetheless remain of a broad relation, hence their inclusion here. Others may disagree. But is is my listing... ‘Of vision interest’. Typically, of lesser mathematical interest. Broadly, this can be described as a side interest of mine (not that I am active in the field), in which vision, and related matters, are studied. Such matters are thus likely of a lesser degree of interest to the typical reader here. As such tessellation, even when it occurs here, which is rarely, is insignificant. However, one aspect relating in a more obvious way is figure and ground. Within a broad tessellation interest, this field nonetheless remains of a broad relation, hence its inclusion here. Others may disagree. But is is my listing...
Abas, Syed Jan and Amer Shaker Salman (with forewords by
Ahmed Mousafa (Arabic calligrapher) and Sir Michael Atiyah). Small format hardback, 396 pp. From p. 140 onward, of diagrams only. A scholarly, although still popular account of Islamic tilings. I like this book more than most others on the theme, which generally lack rigor. Snippets of interest include: Khatem Suleimani (eight-pointed star and cross, Soloman’s Seal) pp. 14-15. This is also known as ‘Breath of the Compassionate’, in Chorbaci. However, this appears to be ‘unofficial’ titling; upon searching using Abass’s term, there is next to nothing, and what there is merely refers to Abbas. A further oddity is the description caption of ‘Soloman’s Seal;’ this generally refers to a pentagram of hexagram, rather than this eight-pointed star. Fig Leaf (Maple Leaf) pp.102. has a good bibliography, with a few references not given elsewhere. No Cairo tiling. Wikipedia gives: The Seal of Solomon (or Ring of Solomon; Arabic: خاتم سليمان Khātam Sulaymān)
Abbott, David (general editor). Popular account of a scientific series (includes Astronomers, Engineers and Inventors), with here mathematics. Has a glossary and index. Many entries on geometry. That said, most entries are outside my area of direct interest and understanding, but it all still makes for pleasant read.
Abbott, P. 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.
Abbott, P. and C. E. Kerridge. Textbook, somewhat advanced. Of no practical use
Aczel, Amir D. Popular account of the historical quest; many digressions and good yarns.
Adams, D. M. 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.
Juvenile, 56 pp. 8–11 year-old range. No tessellation. Oddly, not structured at all, being without introduction and contents. Broadly, ‘pictorial mathematics’, of a wide range. Note that Adler was also active in the field of adult mathematics, and was a prolific author. From Wikipedia: A book Adler wrote for adults
in 1958,
————. Of no interest! From a library sale, on the off-chance of possible interest. Said to be of an intermediate level, not technical, but not too simple. No tessellation.
Agostini. Franco. Minor Escher text pp. 80–81,
————. Escher’s
Ahrens, W. 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. Small format paperback, 62 pp. A Bluffer’s Guide per se can be seen in many other subjects. Various topics and biographies of mathematics covered, briefly, with a dry wit. As might be imagined, a popular account, albeit diagram free. No tessellation/Escher. Of interest p. 39, on the Coriolis effect, on the fallacy(?) of water spiraling in different hemispheres. Ainsley asserts that it is due to the bath shape. To investigate. Of coffee-time reading only.
Albarn, Keith and Jenny Miall
Smith. 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 credibility. Minor aspects of tessellation, within ‘perception’, pp. 40, 43 and Islamic design, pp. 66–67. Appleton, Le Roy H. Indian Art of the Americas. Charles Scribner Sons, New York, 1950 (Internet Book Archive, one-hour loan) (7 June 2021) From a reference in Tilings and Patterns. A brief mention of the book and an illustration on p. 329 in the context of folk art, with two others. Numerous colour plates on patterns in the broad sense, in three sections, but nothing of any real significance per se as regards tilings. Alexanderson, Christopher, Sara Ishikawa and Murray
Silverstein. From a reference of the architecture site Henn, in relation to a mooted parquet deformation reference. Upon research, I found the book as a PDF. A weighty tome, of 1,171 pages! Much to my annoyance, after viewing the whole book, I was not able to find the reference! If there is a parquet deformation reference, it can only be most minor. However, whilst searching, I found much of the book most interesting indeed in a general sense, and ideally I would very much like to read this (ideally as a book, rather than a pdf). However, the sheer length puts me off (with time involved), as good as the material appears to be! Further, I then looked more on the background of Alexanderson, of whom previously I was unaware of. I then became he was still alive, had a website (with in situ tilings), and with more books to his name, of which I notice his interest in tilings per se. His name then began to appear in tiling papers. Likely now, fully primed, I will find references to him in existing papers.
Amiraslan, I. Anderson, Fiona. Tweed (Textiles that Changed the World). Bloomsbury Academic, First edition 2016 Google Books (March 2019) Textile tessellation interest. Specifically concerning the Shepherd's Check and Sir Walter Scott’s supposed popular wearing as trousers, pp. 31–34. In short, Anderson largely debunks this oft-made claim
Anderson, Paul and Deborah Curry. 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
Andrew, H. E. Laye, Although not a book on mathematics, including on this listing as it has a tiling, of overlapping circles, of a minor nature, p. 97, of which I briefly studied (a single sheet). As such, inconsequential, in both mathematics and study thereof. 432 pages.
Angel, Henry. 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. 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.
Anon. From a reference on a 17 January 1989 sheet. However, upon looking for the exact title, there is no book with this name that correlates to the date of study. Perhaps this was rather a chapter title? Whatever, the study was inconsequential, of just a tracing of a jigsaw puzzle in outline.
Anonymous. Small format paperback, of 96 pp, brought out at the height of this Rubik Cube spin-off craze. A brief, single page introduction, followed by pictorial instances of representational shapes that the Magic Snake can be formed. No instructions as such, save for two instances.
Anonymous. From a reference of early maths studies, of 1986-1987.
Anonymous. From a reference of my early maths studies, of 1986–1987.
Anonymous. From a reference of my early maths studies, of 1986–1987 (17 December 1986).
Anonymous. From a reference of my early maths studies, of 1986–1987.
Anonymous.
Anonymous.
————. The 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. 274–284, 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’ (Note the year commonly given, 1964 (Locher, Schattschneider), 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,
————. Juvenile. Occasional polyhedra, no tessellation.
————. Small-format ‘booklet’ 48
pages. Escher prints and minor essay pp. 25–28: Also see a later companion booklet, of 1988.
————. A series of ‘work card’ packs: Area (contains the Cairo pentagon, without reference to Cairo), Similarity 1, Similarity 2, Number Patterns, Topology, Number Patterns.
————. Substantial small format paperback, of 715 pp! Academic in tone, although said to be, in the publishers note (p.6), as ‘… intended for the man in the street…’! However, this is way beyond the stated audience. Formula biased. No tessellation. Nothing that can be said to be recreational. Kepler’s star polyhedra pp. 270–271. Of only possible reference use. I have no plans to re-read.
————. Advanced juvenile. Popular account on shape and number, with much of interest. No tessellation though!
————. Patterns only, no text. Occasional tessellations
————. Looks like tour guide book (I also have another, different book of the same title) no date given, perhaps page torn out…
————. Tilings p. 55, one diagram of octagons of interest.
————. 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 among general wall paper type patterns.
————. Small footprint booklet, 48
pages. Escher pp. 20–31,
Appleton, Le Roy H. Indian Art of the Americas. Charles Scribner Sons, New York, 1950. Internet Book Archive, one-hour loan (7 June 2021) From a reference in Tilings and Patterns. A brief mention of the book and an illustration on p. 329 in the context of folk art, with two others. Numerous colour plates on patterns in the broad sense, in three sections, but nothing of any real significance per se as regards tilings. Apsley, Brenda (Devised by). 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
————. (Devised by). See above.
Armstrong, Tim. Square format paperback, 56
pp. Gives instructions for composing geometrical illusions from acetate overlays with a series of grids, designed to be cut out and experimented with.
Text is light. Not advanced in any way. No tessellation. To what extent these
ideas are original with Armstrong is not made clear. Also see his other book, Briefly studied in 1991, although not to an extensive extent. Of mild interest previously, but perhaps less so now (2018), and for a long while.
————. Not strictly mathematical, but has the occasional crossover.
Arnold, Arnold. As such, this is on game theory, and is of a heavy read, overwhelming of text, 431 pp., with mathematical aspects in the appendix. Likely obtained, for a bargain price, on the off chance of later usefulness. However, it has not proved so! I doubt very much if I even began to read this, never mind the whole book. Even more so today, I simply do not have the time to read. I do not recall any references to Arnold or this book. However, there is indeed a true board game link; he designed the Parker Brothers logo. From Wikipedia: Arnold Ferdinand Arnold (February 6, 1921– January 20, 2012) was an author, game designer and cyberneticist, known more for the fame of his relatives and wives in later life. His first and only legal wife, Eve Arnold, was known for photography. His second partner, who he never married, was writer Gail E. Haley. Arnold's two brothers-in-law were Theodor Gaster and Peter Drucker. … Arnold followed his eldest sister to the United States where he gained work as a writer and cartoonist. He was drafted into the U.S. military in 1941… Arnold was also a successful and well known advertising and commercial designer, and created the famous Parker Brothers swirl logo, first used in 1964. He created and designed many innovative educational and teaching games for leading game designers through the 1960s. He also designed classical record covers for EPIC Records during the 1950s. … During the 1980s and 90's, Arnold published several books, but never again had a financially successful career. He moved back to Petersfield in 1998, where his health rapidly declined. He died in 2012, from complications of sepsis and pneumonia.
Arnold, George and
Frank Cahill. The 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. Tessellations p. 130, barely worth the mention. Textbook.
Ashurst, F. Gareth. Seemingly briefly studied, possibly of just a single sheet, likely, as the discussion would have been of a more advanced nature, with as I recall biographies of advanced mathematicians. However, some pages were more accessible than others, with space filling curves, of which I copied the diagrams and text verbatim. However, there is nothing original here on my part. The book has long been deleted from the library stock, and of which although it available of an accessible price, £7.79, I am not in urgent need of it and I am not actively pursuing this, no matter how ideal it might otherwise be. Audsley, W & G. Outlines of Ornament in the Leading Styles. London, Samson Low, Marston, Searle, and Rivington, 1881. Internet Book Archive (14 July 2021) Subtitled ‘Selected from Executed Ancient and Modern Works. A Book of Reference for the Architect, Sculptor, Decorative Artist, and Practical Painter’. From a reference in Tilings and Patterns. See p. 14 (introduction). The book is one of many of their generic listings on pattern and design. It does not as such appear to have been discussed in the main text. As such, the book is typical of the day i.e. Owen Jones. Nothing in the way of the diagrams appears new, or has tilings that are of particular interest (Cairo, houndstooth etc). Only skim viewed. Ideally I would read and study, but I have no time. Augarde, Tony. Not strictly mathematical, but related in a sense, with word play. 26 chapters. d'Avennes, Prisse. L'art arabe d'après les monuments du Kaire depuis le VIIe siècle jusqu'à la fin du XVIIIe. J. Savoy & Cie editeurs (Paris) 1877, 296pp. Downloaded from Bnf Gallica (20 July 2020) Translated: Arab art from the monuments of Cairo from the 7th century to the end of the 18th century From a reference in Tilings and Patterns and mentioned in the minor listings on tilings in every civilizations and cultures, p. 463, but apparently not in the main text of the book again. Somewhat of a letdown in terms of tiling matters. Mostly text rather than illustrations. And mostly on ornament rather than tilings. What tilings there are have essentially been seen in other like books of the day.
From reference in MacMahon. As this title suggests,
this is wholly on numbers; no tiling whatsoever.Bager, Bertel. Nature as Designer. A Botanical Art Study. Reinhold, New York, 1966. Translated by Albert Read. Foreword by Harry Martinson. Originally published in Sweden under the title Naturen som formgivare, 1961. 175pp. (Viewed on Internet Archive, one-hour loan, 28 July 2021) From a reference in Tilings and Patterns and mentioned in the listing ‘Patterns in nature and science’, p. 14, but is not discussed further in the text. Unashamedly a pictorial book, and without mathematical tilings as such. Lavishly illustrated. Would be an interesting (and worthwhile) read, but I don’t have the time! Bain, George. Celtic Art. The Methods of Construction. Dover Publications, New York, 1973. First published by W. MacLellan, Glasgow, 1951 (Viewed on Internet Book archive, one-hour loan, 3 August 2021) From a reference in Tilings and Patterns and mentioned in the listing ‘patterns and design’, p. 14, and briefly in the main text pp. 214 and 234 but is not discussed further. Skim viewed thumbnails only. Nothing in the way of tiling as such, albeit with obvious crossovers. As expected, of limited interest. I do not intend to pursue this further. Bain, Iain. Baker, Lyndon et al.
Ball, Johnny. Soap bubbles p. 59.
————. For children. An assembly from the BBC TV children's series, of ‘Think of a Number’, and spin-offs, ‘Think Again’, ‘Think Backwards’ and ‘Think This Way’ with the material assembled as a book. As such, there does not appear to be anything original here, with Martin Gardner credited as the main inspiration. Of most interest, relatively speaking, is pp. 70-71, on tiling with quadrilaterals.
————. 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 special interest include the Golden Ratio, pp. 50-51,
where he gives, for me a new explanation. Kepler pp. 306–314 plate in
Ball, Phillip. Chapter 4, pp. 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. Surprisingly light on tessellation, pp. 105–107 only.
Banchoff, Thomas F. 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. Dudeneyesque.
Barr, Stephen. Largely popular account, although I do not actively pursue the topic. Of most note is Chapter 3, ‘The Shortest Moebuis Strip’ pp. 32–39 and Chapter 7, ‘Map Colouring’ pp. 88–97. The Moebius idea is so simple, and yet I had never thought of this! Some of the material is taken from others.
Barratt, Krome. 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 pp. 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. Small format paperback, 317 pp, of limited interest; semi-popular, not easily described, of mostly ‘mathematical philosophical musings’. Barrow is perhaps better known as an astronomer. Text heavy, with only occasional diagrams. No tessellation, Escher. Numbers from different countries p. 44, Four-colour conjecture pp. 227–234. Overall, it’s ‘interesting’, but the time involved now (2018) to re-read this would be disproportionate as to any benefits gained, of which I doubt.
————. 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
Beard, R. S. (Colonel) 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 Beaumont, Roberts. Color In Woven Design. Whittaker & Co, First Edition 1890, Second edition 1912 (Internet Archive.org) (2019?) Textile tessellation interest. Of houndstooth and weave interest. Beer, Arthur and Peter Beer (editors). 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. Use of Escher's
Bekkering, Betsy and Geert Bekkering. 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. 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.
Bell, Marc. 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. 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!
————. Small format paperback.
Bellos, Alex. A personal wander around mathematical aspects of interest to the author, of an overwhelmingly popular level. Occasional references to Escher, pp. 244 and 392 hyperbolic geometry, with Circle Limit IV. Phi, pp. 299-301 (and colour plates), with Gary Meisner interview. Martin Gardner pp. 250-253, plus lots of general interest. Sam Loyd pp. 237–240, Henry E. Dudeney pp. 240–242. Typical Bellos, of a delightful read.
————. Described as, in the introduction, ‘… a curated collection of 125 brainteasers from the last two millennia, linked with stories about their origins and influence.’
Bellos, Alex and Edmund Harriss. Mathematical coloring book, not paginated. Of note is my contribution to this, of the fish tessellation on back cover and two works inside; ‘Nested Fish’ again, and ‘Interflocking Birds’ (Bellos' witty description). Of note is Harriss' parquet deformation (with likely Bellos title) ‘De-four-mation’, of four non-periodic tilings positioned in a corner, which morph left to right and top and bottom. Beat that if you can!
Belur, Ashwin and Blair Whitaker. Small format paperback, of just 32 pp. Gives instructions as to Rubik’s Magic, a latter day addition to the cube theme, perhaps best described of a folding rectangular 2 x 4 array and ring premise. From memory, I do not believe I have ever tried ‘seriously’ to solve this. Seeing as I was unfamiliar with
Belur and Whitaker I had a look on the web. Apparently there was controversy
with Rubik, despite him writing the foreword. From
Bergamini, David and the Editors of TIME-LIFE Books. This is really ‘The Story’ of
mathematics, rather than of an expository nature as the title implies. Much
of interest, although detailing this is not the most straight forward task. No
tiling. (False) references are made to the golden ratio appearing in paintings,
pp. 94–97, of which Mario Livio in This is a paperback, also see hardback, in possession.
Beyer, Jinny. Jinny Beyer, a patchwork designer, and not, by nature, a mathematician, or at least a natural one, gives her thoughts on designing tessellations, and much more than the title otherwise suggests. Her background pervades the book, of a patchwork premise. Strictly, I do not know what to make of this. There is the potential for a good book here, but this is not it! In short, I think she addresses too many aspects beyond her understanding (albeit well-intentioned, with the non-mathematician patchwork worker in mind), of which she attempts to cover ‘all’, from history to basics to Escher and more. There are many aspects here that I have issues with. To begin, even the title! There are no ‘secrets’ as such in the sense of information being withheld. Another is the text is lacking in exactness in various places, too numerous to list all. I content myself with her definition of a tile, illustration 1.3, p. 4. Chapter 10, a digression to the Escher aspect, is a veritable disaster. She simply does not understand the issues. Anyone who can be proud of ‘houses’, pp. 206 and 222 reveals her lack of understanding of them. Likely a house, being a popular patchwork motif, was thus obviously chosen, but this does not excuse poor practise in design. The other tessellations, some by others, generally lack merit. However, a cat (by Beyer) ‘Tessellating Sue’ is at least respectable. The ‘pure’ tilings are better in terms of worth. Chapter 11, on Metamorphosis, is not really as such; the transitions are far too abrupt, being nothing more than abutments. Aside from the content per se, the book lacks an index, and so thus finding specific aspects is trying. It really is most frustrating trying to separate the wheat from the chaff here! Interestingly, the cover and title pages features the Pólya tile C4, but without my bird motif. Has many instances of Escher’s periodic drawings: Birds E128; E120/121 Birds and Fish; E24 Birds and Fish E25 Reptiles, all p. 3; Reptile E25, p. 127; E73 Flying Fish, p. 134; E128 Birds, p. 203, E90 Fish, p. 205, Fish and Boat E72, p. 219; E120/121 Birds and Fish, p. 220; Fish E119, p. 221; Bat/Bird/Bee/Butterfly E81, p. 224, E85, p. 225. Prints: Reptiles, p. 228, Metamorphosis I, pp. 236–237. Sketch: wall mosaic in the Alhambra, p. 202. Cairo tiling, but not attributed as such, p. 144.
Bezuszka, Stanley, Margaret Kenney and Linda Silvey. School age level, with ‘activities’. ‘Skew’ Cairo tiling, on triangular grid, p. 38. No Escher-like tessellation discussion at all.
Bibby, John.
Bigalke, von Hans Günther and Heinrich Wippermann.
Bigalke, von Hans. Birkhäuser Verlag, 1988 Translated: Heinrich Heesch: Crystal Geometry, Tiling, Four-Color Research, 320 pages.
Billings, Robert W. and Robert Williams. From a reference in Bradley. Quoted on p. 6. Of limited interest, if at all. The book is ostensibly about tracery designs, something of which is strictly outside of tiling matters. Tracery (rather than tiling) seems to be Billings’ main interest, he has one other book, at least, on the subject.
————. From a reference in Bradley. Of limited interest, if at all. See comments above.
Bilney, Bruce Gift of Bruce Bilney. Self-published booklet of 32 pages. Promoting his own ‘Spectrochrome’ Platonic models. Occasional digressions from polyhedra, with stereo and tessellations.
Bingham, Jane. Implied as for teenagers on the back cover. A look at various aspects of illusion art, of 56 pp. A somewhat lightweight treatment. M. C. Escher features prominently, of 16-17 (primarily), 20-21, 35, 40-42 (in passing) and cover (Waterfall). However, the research is particularly poor here, with Escher described as from Belgium! And the ‘find out more’ page gives J. L. Locher’s name as Locker, and misspells Doris Schattschneider without the n. From this, likely they will be other errors throughout too. The book is perhaps atypical of others, in the illusions shown many I have not seen before, and with a name I have not seen before, notably with John Kay, p. 39, of ‘The Lawyer and the Client’, although I am familiar with the illusion. The section ‘puzzling patterns’, pp. 40-43 discusses tessellation, with an illustration of Patrick Snels' work. Overall, even for a teenager, far too lightweight.
Birtwistle, Claude. A book that was briefly studied in 1987, but is of no consequence. Unavailable, save for a mad price, £180! Black, Mary E. the sett and weaving of Tartans. Lily Mills Co, 1959 PDF (February 2019) Textile tessellation interest. A small book, of 47 pp, readable. On tartans primarily and despite the title, has much on houndstooth-related matters, notably with the Shepherd's Check, pp. 9-11. Very nice. From Wikipedia: Mary Ellouise Black (1895–1988), an occupational therapist, teacher, master weaver and writer, created almost single-handedly a renaissance in crafts in Nova Scotia in the 1940s and 1950s. Her best-known book, ‘’The Key to Weaving", was published in 1945 and has since run to 3 editions and numerous printings. Its clarity is without parallel, and, more than half a century later, it remains a handweaver's prime source of information. Blackie, Alex B. Wood Pavement; Its Origin and Progress, London, Sherwood, Gilbert and Piper, 1843. Available Online. (c. 8 May 2019) Of pavement interest. On wood block paving. Everything one would wish to know! (Skim Read). Reference to hexagonal blocks, pp. 25–26, 28, 35–36, 39, ‘41’, 48–49, 54, 56, 72. David Stead mentions.
Block, J. Richard and Harold E. Yuker 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.
Bonanni, A. P. P. Circle packing reference, as given by D’Arcy Thompson
Bourgoin, J. No Cairo.
Boles, Martha and Newman, Rochelle. 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. Note that this a book on patterns in the general sense; that is, it is not focussed on tiling.
Boles, Martha and Newman, Rochelle. Similar in spirit to Book 1, with compass constructions. Of the two, this is more directly related to my interest, with chapter 4 on tiling, pp. 130–169, and other tiling instances scattered throughout the book.
Bolt, A. E. and J. E. Hiscocks. One book of the seven-part
‘Mathematics for the Majority’, series, of which I have two. The book seems to
have been compiled by a ‘project team’, with one primary author stated. The
books are stated as ‘Chatto & Windus for the Schools Council’, which thus
gives the intended audience. The topic of this book is out of my mainstream
interest, but it still has isolated aspects of interest. Also see
Bolt, Brian. 130 ‘popular’ mathematical puzzles, with answers. Stated as from ‘a resource book written for teachers’, but the title is not given. Possibly, this is the reference below. Also states ‘many of the puzzles have a very long history, other are original…’. However, upon an admittedly cursory look, I cannot see any that I am not familiar with. No plans to re-read, being one of many of the same compilation nature.
————. 154 activities, of a recreational nature, pitched at a middle school level, with answers. Especially see Activities 39 Tessellations, p. 28 and Activity 40, Tessellations and art, 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.
————. Seems to be, as with his other works, a compilation from other sources.
Bossert, Patrick. Small format paperback, of 112 pp., brought out at the height of the Rubik Cube craze. Simple step-by-step instructions. However, although I have likely tried this at the time, this was to no avail! The situation has not progressed since then, not that I have tried for a long while. As much as I would like, time forbids a new round of study. I see that Bossert was just twelve-years-old at the time! What became of him is not clear. Bourgoin, Jules. Grammaire Élémentaire De L'Ornement: Pour Servir À L'Histoire, À La Théorie Et À La Pratique Des Arts Et À L'Enseignement. Delagrave, Paris, 1880, 207 pp. (Internet Archive, 24 August 2021) Translated: Ornamental Elementary Grammar: For Use In History, Theory And Practice Of The Arts And Teaching. In French, seemingly no English translation. From a reference in Tilings and Patterns, p. 657, and mentioned in the listing of failure in the context of a systematic mathematical study p. 12 (not discussed further in the text). However, ‘failure’ here is in relative terms, as according to Grunbaum and Shephard stricter structures; as is, there is much here worthy of study. Quite exactly what Bourgoin is striving for here is unclear, as I am let down by my French, as well as the ‘inconvenience’ of reading a PDF. However, it is clear that this is a very nice book indeed. A (simple) combinatorial approach to tiling is adopted, similar in style to the later work of Percy MacMahon in New Mathematical Pastimes, but whether all the tiles will tile is unclear. Indeed, there is not a tiling diagram as such in the book! Boyer, Carl B.
Boys, C. V.
Bradley, Amos Day.
Bradley, Chris. Possible Cairo tile sighting at Azbakkiyyah Gardens, p. 28.
Brandreth, Gyles. Not a ‘big book’ at all; standard paperback size!
————.
————. A part original, part from other sources small format paperback compilation, as is made clear in the foreword, including puzzles of Lewis Carroll, Sam Loyd and Henry Dudeney, although the attributions not made clear in the puzzles themselves. Brandreth’s ‘originals’ seem few and far between. Has 20 various puzzles within the full remit of the term. Dissection puzzles pp. 39–43, Geometric Puzzles pp. 54–56, Pentominoes pp.87–92. In style, the book is similar to many other compilations. In short, a fun work, not of a scholarly nature, having not seen it referenced.
Brest, Hillary et al. Various activities and investigations of the Stella Octangula, including blackline masters (nets) Also see companion book
Brett, Michael, and Werner Forman. (Seen c. September 1987, but not in possession). Note that this book (title only) was recorded on a menu card, stated from the central library, in conjunction with other Islamic tiling books of the day, 1987. There is no recorded studies as such. I cannot now recall this in any way.
Briggs, William. Typical generic maths text book of the day; way beyond me, on Euclid, Algebra and Trigonometry. One of many that I have; simply, one would have sufficed. The reason for obtaining the book was to be able to look up any maths/geometric construction as and if required, but I do not believe that I have used this in any way.
Bringhurst, Robert. The Elements of Typographic style Second edition. Hartley & Marks, publishers. 1992 (3 November 2018) Some ‘page size mathematics’ Chapter 8, pp. 143–178.
Briscoe, Susan. The Ultimate Sashiko Sourcebook. Patterns, Projects and Inspirations. David and Charles 2005. Cleethorpes library. First saw a few years ago, but never got around to borrowing (16 February 2019) Simply stated, a book on ‘Sashiko’, a term of Japanese hand stitching. It is replete with tiling images. Especially see p. 67, ‘Yatsude asanoha’ (eight-lobed hemp leaf) from which a Cairo tiling can be derived. P. 87 has a tiling that can be shaded as a outstretched human figure! Furthermore, for the first time (I believe) I have realised that what appears to be traditional Japanese patterns of an isometric appearance are not so, but rather are drawn on a rectangular grid. From the author’s website: Sashiko (pronounced shash-ko) literally meaning 'little stab' or 'little pierce' is a traditional Japanese hand stitching technique that can be used to strengthen, repair, add warmth to or simply decorate fabric refers to the small running stitch that is worked to build up distinctive decorative patterns, of which there are hundreds. The book begins by exploring the origins of the technique to strengthen clothes and to make them warmer. Getting Started describes everything you need to begin stitching, including selecting suitable fabrics and threads, marking out patterns on the fabric, as well as the stitching technique itself. Ten project chapters show how easy it is to use sashiko patterns to make beautiful items for the home. The main focus of the book is the step-by-step detail in the pattern library, showing you exactly how to mark and stitch each individual pattern with ease. Finally a gallery of work by contemporary Japanese textile artists from Yuza Sashiko Guild provides extra inspiration. Although inself, from the title alone, one would not expect this to be of any real interest, the book is replete of tiling patterns, and so worthy of study. Further, as such, it is invaluable (i.e. readable) in the Japanese-English context. Biography: Susan Briscoe is a textile artist, quilter, teacher and author of numerous books, including Japanese Quilt Blocks to Mix and Match, The Ultimate Sashiko Sourcebook, 21 Sensational Patchwork Bags and 21 Terrific Patchwork Bags. She is also a specialist dealer in Japanese textiles, Kimono and Kimono fabric. Brockett, Anna. Juvenile, 12+. No Cairo.
Brown, James. 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.). 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. 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. The thinking behind teaching. No tessellation.
Britton, Jill and Walter Britton, 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. Tilings occasionally discussed, Alhambra, Chapter 5, The Music of the Spheres pp. 155–188. Buchsbaum, Ralph. Animals Without Backbones. University of Chicago Press. Eleventh Impression 1947. First published 1938. (May 2019). Available on the Internet Archive: https://archive.org/details/in.ernet.dli.2015.475221/page/n185 Of peripheral Escher interest. Said (and confirmed by Sherry Buchsbaum, the daughter of the author in a reply to a blog posting, below), to be the book that Escher used for his Flatworm drawing references. Although obviously non Escher per se, it is included here in relation to him. From Sherry Buchsbaum: Escher was definitely influenced by Elizabeth Buchsbaum's drawing of planaria. This can be seen in the chapter heading drawing for Chapter 10 and 12 and following drawings in Animals Without Backbones... Chapters 10 p. P.109, Chapter 12 p. 124. From Amazon: Animals Without Backbones has been considered a classic among biology textbooks since it was first published to great acclaim in 1938... Brückner, Max Frequently quoted in tiling concerns, such as by Schattschneider. On polyhedra. Highly technical, with much abstruse text, albeit liberally illustrated with line drawings, and latterly plates and polyhedral models. Of interest as regards tiling p. 109 dual tiling (Cairo) p. 158.
Buckwell, Geoff. 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?
———— . 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. From an Escher reference in Schattschneider’s
Burden, I., J. Morrison, and John Twyford. As such, there are various uncertainties here as to the book, borrowed from Grant Thorald library, due to it being poorly referenced of the day. Upon a internet search, I have only found one other book with this title, but as this is a subsequent publication to the date recorded here, 17 January 1989, it cannot be this one. Further, I am not even sure of the title – a page number precedes the title, and so possibly this is a chapter reference instead. No publisher was given. Whatever, the book can hardly be of any importance; the study, on a 10 January 1989 sheet headed by A. Racinet ornament studies, consists solely of a well-known jigsaw tiling seemingly traced in which I remark upon the opposite side square feature. Burn, Bob. As sent by Bob Burn. Borrego, John. Space Grid Structures. Skeletal Frameworks and Stressed-Skin Systems. Cambridge, M.I.T. Press, 1968, 200pp. (One-hour loan on Internet Archive, 12 August 2021) From a reference in Tilings and Patterns and briefly discussed in passing on p. 111 (as regards a blatant error on the numeration of Archimedean tilings), but the book is then not discussed further in the text. In the discussion Grünbaum & Shephard take Borrego to task for an error regarding Borrego’s assertion of an ‘extra’ Archimedean tiling and ‘documented’ by a drawing. As such, as regards tiling, there is very little here, and what there is is of just basics, almost of first principles, not to mention the error outlined above, which does not exactly fill one with confidence in the content in the round. Pp. 132, 134–135, 194–197 have basic tilings. The book is typical ‘structural topology’. A skim view proved more than sufficient; I am not planning on pursuing the book further.
————. 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. 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.
Burrett, Anthony. Small (square) format paperback, 66 pp. From the 200-book Project Book series, introducing all kinds of pastimes from brass rubbing to building a home museum, with here mathematics of book No. 110. A handful of titles blossomed into a range of two hundred as the lavishly illustrated booklets caught on. An emphasis is on the practical aspect. The series is aimed at school children, c. 12 years of age. Mostly about time per se. Polyhedra pp. 46–47, Minor tilings pp. 48–49. However the treatment is so basic as to be of no consequence. Also see book No. 101,
Cadwell, J. H. 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. 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. 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.
————.
Campbell, Cyndie. 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.
From a reference in Bradley. Book quoted on p. 12. Somewhat
of a let down; the book does not have a single diagram!————. 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. 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, 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. 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,
Chamber, W. R; Murray, John. 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. Juvenile. This seems related
in someway to the
Chauvan, Sumi Krishna. 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. 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. Has an Escher print on the
front cover,
Cook, L. H. Longley-. 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. 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.
Coffin, Stewart T. Delightful throughout. Also, two-dimensional puzzles and dissections are briefly discussed, Chapters 1 and 2.
Cohen, Jack; Stewart, Ian. Somewhat advanced.
Colby, Averil. 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. Includes Escher’s
Cole, Drusilla (General Ed).
Conway, J. H. Of limited interest, mostly advanced maths. Conway, J. H. and H. S. M. Coxeter. ‘Triangulated Polygons and Frieze Patterns’. The Mathematical Gazette Vol. 57, No. 400, June 1973, pp. 87-94. (8 July 2019) Academic. Despite an ostensibly popular account by the title, too advanced for me. No diagrams. The article continues into the next issue.
————.. ‘Triangulated Polygons and Frieze Patterns (Continued)’ The Mathematical Gazette Vol. 57, No. 401, October 1973 pp. 175-183. (8 July 2019). NOT SEEN Academic. A follow-up to the above.
Conway,
J. H. et al. 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. Cook, Jill. Ice Age art: arrival of the modern mind. British Museum Press 2013, pp. 108-109, 134 (17 August 2019, but known a few years previously) Of historical tiling interest. Upon seeing a post by Robert Fathauer on Twitter of 10 August 2019 on a 2,000-year-old (regular) hexagonal paving at the Great Temple, Petra, I resolved to revisit an old hexagonal tiling sighting myself (a few years back), details (title, author, date) long forgotten, in a book at Cleethorpes library, as above. I now see that this is on the Eliseevichi, Russia, tusk artefact, with a c. 12,000-15,000 BC dating, now in the Peter the Great Museum of Anthropology and Ethnography (the Kunstkamera), Russia. This concentrates on the historical significance of the tiling without any mathematical aspect. Upon seeing this book again, and following up the sighting up, of the museum, and articles by (medics) Geoffrey Schott and Clare Caldwell, I posted to the Google tiling group on the potential of an exciting discovery, this has not been discussed in the mathematical literature as a tiling, as far as I was aware. However, this met with only lukewarm response, with only two replies, of an additional earlier artefact, the Blombos Cave, South Africa. Corbalán, Fernando. The Golden Ratio. The Beautiful Language of Mathematics. Published by RBA Coleccionables, S. A, 2012. An English translation of a Spanish work (7 June 2014). In association with One of a series of popular maths books, originating from Spain. The background is that a group of Spanish Mathematicians have written a comprehensive set of popular maths books, which have proved so successful that they're being translated into other languages, including English. The team behind the series have joined up with The Times newspaper and Marcus du Sautoy to present the series to the British audience. As such, a nice treatment on the Golden Ratio, although I do indeed have, on occasion, serious concerns. Unsurprisingly, given a pentagon underlay, there is much of interest here. Has occasional tiling aspects. 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. Beforehand, Corbalán was a new name to me. Amazon: Corbalán is a mathematician expert in this subject having written several books on the golden ratio or related themes.
Cordova, Chris De. 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.
Cotterill, Rodney. Although not a maths book per
se, included as it has Escher aspects. Page 63 E97 Bulldogs, E85, Lizard Fish
Bat; 81
Courant, Richard and Herbert Robbins.
Cowen, Painton. 144 pp. A4 paperback. Popular account, with diagrams and photos. Although I have no particular interest in rose widows per se, there is a decided geometrical element to this, and so thus likely chose to purchase, in Sheffield, on the basis of ‘buy or lose’ of the day, this preceding ready availability on the internet. However, I do not recall any direct study from this. Time forbids a dedicated re-reading. Pages of interest include p. 93 on Honnecourt with tilings. Geometrically of interest is ‘Divine Geometry’, pp. 121–127. Incidentally, suitably recalling Honnecourt, I had a look on the web for any more tilings of his, but it can quickly be seen that tiling was only a minor interest. Also see a more substantial publication, The Rose Window Spendour & Symbol by the same author.
————. 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. A collection of essays; indispensable.
Coxeter, H. S. M. 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.
————. Academic. Escher pp. 57 (Horseman E67) - 59 (Beetles E91), 63. Very brief text. First studied, or at least recorded 25 January, and 5 February 1988 upon ordering from the library. Unsurprisingly, very little is accessible to me.
Coxeter, H.
S. M. and S. L. Greitzer.
Cracknell, A. G. and G. F. Perrott. 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. A minor study, in which the crystal studies are shared with other books of a like nature
Craig, Diana. Although nothing whatsoever on maths, included here as a tenuous interest as regards cluster puzzles, specifically of pp. 42–43. I might just add that Arcimboldo is an artist I much admire, with his work of an imaginative nature, although I have not made any special effort to study his work. This book here, of a popular nature, of a 54-book series (including Escher), found by a casual browse in a charity shop, at least serves as an introduction pending a more detailed work being found.
Crane, Walter. Minor tessellation pp. 89, 128. Arabic designs pp. 213–217, otherwise mostly of ornament. Nothing of any significance.
Crilly, Tony. Popular account from across the spectrum of mathematics, 1. Zero, 2. Number Systems, 3. Fractions etc. However, there is no tiling.
Critchlow, Keith. 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.
————. Somewhat quirky; Islamic patterns interspersed with nonsensical cosmological and philosophical speculations thereof.
Cromwell, Peter R. Escher pp. 2, 171–172 (sketch of a cutaway view of small stellated dodecahedron), 239, 251, 258. Mostly minor text, in conjunction with polyhedra.
Crook, Diana (editor). Alice Dudeney’s diaries, with
Henry Dudeney puzzle interest. Quite how this publication came to my attention
is not clear, but likely from Federickson’s writings; it is mentioned in
Crowell, Robert A. Parquet deformations.
Delightful. Works by Jacqueline Damino Right,
Cruys, Sander Van de, and Johan Wagemans. ‘Putting Reward in
Art: A Tentative Prediction Error Account of Visual Art’. Non-tessellating article, with a one-line mention of Escher, p. 1042, illustration with Day and Night.
Cundy, H. Martyn and A. P. Rollett. 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) Curbera, Guillermo P. Mathematicians of the Word, Unite! A. K. Peters, Ltd. Wellesley, Massachusetts First edition 2009. (12 November 2020, PDF) A history of the International Congress of Mathematicians, from the beginning to the present day. Escher p. 138 (broadly in passing), and pp. 252–253, in-depth, of his role in his exhibit at the Stedelijk Museum, 1954. Of particular interest is the following passage in which a new name to me is mentioned, one J. J. Seidel, but without further detail: The organizing committee of the congress—in particular, some of its members such as N. G. de Bruijn and J. J. Seidel—had the idea of having an Escher exhibition as an adjunct to the congress… Upon research (Wikipedia), this is Johan Jacob "Jaap" Seidel, a Dutch mathematician who dealt with geometry and graph theory. It is stated: ...organized an exhibition by MC Escher. Upon an initial search, there is little else on the Escher-Seidel connection. De Bruijn mentions this again in Nieuw Archief voor Wiskunde (New Archive for Mathematics) 5/2 nr. 3 September 2001 and is basically repeated in his tribute ‘Jaap Seidel 80’ in Designs, Codes and Cryptography, 2000, 7–10. Seidel also reviewedM. C. Escher: Art and Science in The Mathematical Intelligencer 10, no. 1 (1988), 69–70, but I don't seem to have noticed/saved this when I had free access to MI! It certainly does not justify the high cost now. There does not appear to be anything else on their interaction or his Escher interest elsewhere.
Daintith, John and R. D. Nelson. (editors, with ten contributors).
The A more advanced treatment, aimed at ‘… first-year university students’, with over 2800 entries and more than 200 short biographies, although nothing, surprisingly, on tessellation! Primarily of text, has few illusions, with much beyond my understanding and interest. A useful occasional reference guide, but nothing more.
Dantzic, Cynthia Maris. Brief looks at design aspects. Much of interest. Leonardo quote p. 308. Numerous Escher pp. 49, 57, 60, 88-89, 103, 137, 252-253. Paving stone with overlapping circle tessellation, of c. 700 BC, p. 48. Mention of
Darton, Lawrence. Davey, Wheeler P. ‘A Study of Crystal Structure and Its Applications’. First Edition New York, London, McGraw-Hill Book Co., 1934. 712 pp. Seen (not downloaded) on Internet Archive (7 January 2020) Of a Donald G. Wood reference (Space Enclosure Systems). Examined thumbnails (in the hope of pentagon tiling), but no tiling as such, with only the most superficial relevance on occasion. Day, Lewis, F. Similar is style to Archibald
H. Christie’s
————. Textbooks of ornamental design. Part of a trilogy,
————. I am more than a little confused here, with a somewhat convoluted series of titles and editions! Has houndstooth-like basket weave plate 11, p. 25, in the subsection ‘1. The Application of Ornament’ in further subsection 3, ‘Where to Stop in Ornament’, simply described as ‘African’, with only the most minimal of explanatory text. First edition, Plate 10 p. 40, as it was plaited and Fourth edition… Would any more pretentious form of art, be so entirely satisfactory for the purpose of basketwork as the ingeniously plaited pattern of Plate 11?’ Of next to no tessellation, which only appears loosely. No further details are given as to provenance. The book is dated 1895, or at least the PDF version I have, of the fourth edition. Part of a trilogy, The Anatomy of Pattern, Planning of Ornament, The Application of Ornament.
Davies, Linda and John Hardingham (designers, no author
stated).
Davis, Adam-Hart. Tessellations pp. 96-97. ‘After Escher’ picture of birds and fish, No. 34, page 97. Juvenile. Davis, C. (Editor), B. Grünbaum (Editor), F. A. Sherk (Editor). The Geometric Vein: The Coxeter Festschrift. Springer, 1981 First edition. (16 June PDF) From a sub reference in Tilings and Patterns. Skim read the whole book. As to be expected, overwhelmingly academic. Occasional tiling articles referenced in the book, notably ‘Uniform Tilings with Hollow Tiles’ by B. Grünbaum, J. C. P. Miller and G. C. Shephard, ‘Spherical Tilings with Transitivity Properties’ by B. Grünbaum and G. C. Shephard, and ‘The Geometry of African Art III. The Smoking Pipes of Begho’, by Donald W. Crowe. Each of these is detailed by the author/s in my listing. Although tiling is discussed, this is typically academic, way beyond my understanding. Only snippets are ‘useful’. The analysis was wholly disproportionate as to any benefits to be gained (as was admittedly expected), but nonetheless, there may have been something, and so I don't unduly begrudge the time spent on this. I now at least know, and can thus rest easy. Note that I checked the (48) author listing with the references in Tilings and Patterns, but there are no others than that given as above.Davies, Paul. Although
on physics, included here as it has occasional recreational maths. Brief
mention of Escher p. 93, within a discussion of Hofstadter ‘s
Davis, Philip J. and Reuben Hersh. 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. Day, Lewis F. Preamble Day, Lewis F. Text Books of Ornamental Design I. The Anatomy of Pattern. London B. T. Batsford 1887, 55 pp., with 35 plates (PDF, Internet Book Archive, 19 August 2021) ————. Text Books of Ornamental Design II. The Planning of Ornament. London: B. T. Batsford second edition 1887, 49 pp., 38 plates (PDF, Internet Book Archive, 19 August 2021) ————. Ornament and its Application. A book for students treating in a practical way of the relation of design to material, tools and methods of work by Lewis F. Day. London: B. T. Batsford. New York Scribner’s Sons 1904, 319 pp. (17 August 2017 Internet archive download) Skim read/viewed. Has houndstooth-like basket weave plate 11, p. 25, in the subsection ‘1. The Application of Ornament’ in further subsection 3, ‘Where to Stop in Ornament’, simply described as ‘African’, with only the most minimal of explanatory text. First edition, Plate 10 p. 40, as it was plaited and Fourth edition… Would any more pretentious form of art, be so entirely satisfactory for the purpose of basketwork as the ingeniously plaited pattern of Plate 11?’ Of next to no tessellation, which only appears loosely. No further details are given as to provenance. The book is dated 1895, or at least the PDF version I have, of the fourth edition. Preface THIS book is based (like "Pattern Design") upon the foundation of an earlier volume. But, though it covers the ground of "the Application of Ornament," now out of print, it covers a larger area. It is really a new book. Here and there a fragment of the earlier one is incorporated in it; but even that has been shaped anew; for it seemed, looking back upon the work of fifteen years ago, there was little in it which could not be more simply said. The aim of "Ornament and its Application" is throughout practical. It appeals, however, less exclusively than some of my books to students of design ; in fact, it is addressed to all who are really interested in ornament. To those not practically acquainted with the subject, it may serve as introduction to that quality of workmanlikeness which to a workman is of the very essence of design. Dearling, Alan and Howard Armstrong. Paperback, 10 chapters, 247 pp. General puzzles and games of all types (serious and fun) for youths, seemingly intended for youth clubs. The format is a title and general discussion. Martin Gardner gets a mention. Largely a rehash of existing games, from a youth club perspective, but still a welcome contribution in that context. That said, there is little here that is original. I have no plans to re-read.
Deboys, Mary and Pitt, Eunice. First seen as a library book, October 1993. Tessellations: cover, pp. 158-160, 278-286. Juvenile
Dedron, P and J. Itard. Eclectic account, slim volume.
Kepler plate from
Degrazia, Joseph. Small format paperback, 159 pp. Gardeneresque. Mostly on number/arithmetic puzzles. No tiling or anything of a geometrical nature.
Deledicq, Andre and
Raoul Raba A little lightweight, of just 64 pages.
Devi, Shakuntala By the calculating prodigy, a throwback to bygone days of human calculators. On number calculations, and how she achieved such prodigious feats of stupendous calculation. One can only stand back and admire. Really of general interest only. Dietz, Ada K. ‘Algebraic Expressions in Handwoven Textiles’. Louisville, Kentucky: The Little Loomhouse. 1949 monograph Advanced! Although there is nothing directly houndstooth here (in whatever capacity), included as this is a landmark work, as ‘seen and noted’.
Dismore, Julian, Compiler. Described on the cover as ‘65 brain-teasers from the popular [Yorkshire] TV series’, although when is not stated, and I’ve never heard of it. Or perhaps I have forgotten! Whatever, a small format paperback, with puzzles seemingly taken from existing instances, framed with Dudeneyesque storylines, but typically much shorter. Dismore is an unknown name to me. The book states that he is an economist among other lighter interests. Simply stated, the book is like one of many of the compilation genre, lacking in originality, and so is inconsequential.
Dixon, Robert.
Dolan, Daniel T.
and James Wilkinson. A partial PC of a library book. A few pages on polyominoes, nothing of any significance or substance. Don, Sarah. Traditional Samplers. Viking, 1986. (16 November 2019) Of peripheral tessellation interest. A general purpose book on samplers, of history to the modern day, although of course tessellation is not generally the premise! However, I have noticed on occasion that samplers do make use of tessellation and so therefore of possible or potential interest. Of occasional historical interest as regards tessellation at the beginning, albeit in general is not to the fore, but rather geometric ornament and bands. Of note is the historical interest, with one sampler of 1598 given (the earliest English surviving instance). The pages refer to pattern books of the 1500s, which I will follow up. Much here is new to me in a general sense. I previously thought a stitch was a stitch, but no! There's Running Stitch, and more exotic, such as Algerian Eye, to name a few! To investigate… As such, investigating the field of samplers as regards tessellation flatters to deceive and seems very much out of proportion as to worth in terms of time expanded. What I have investigated on the subject shows next to nothing, and of which I am not planning to investigate further, at least in a concerted effort. I may still have an occasional look. Donovan, Johnston
A.
Dörrie, Heinrich (translated by David Antin). ‘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. No tessellation as such, mostly of ornament in various forms.
Dudeney, Henry Ernest (edited by Martin Gardner). An absolute classic in the field, but no tessellation as such! Dissection puzzles pp. 114-125.
————. 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!
————. An editorial note states that
the puzzles in this book were originally published in serial form in the
magazine 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) 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) 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!
————. 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. Dürer, Albrecht. Underweysung der Messung mit dem Zirckel un Richtscheit, 1525. (The Four Books of Measurement with Compass and Ruler). Translated as The Painter's Manual. Abaris, New York, 1977, 472 pp. (First saw as The Painter’s Manual in 1993?; not in possession) From the Introduction: "not only for painters, but also for goldsmiths, sculptors, stonemasons, carpenters, and all those for whom using measurement is useful." Anon: The treatise synthesized a number of classical and contemporary mathematical texts with the knowledge of geometry Dürer had accumulated over a lifetime of artistic practice, in order to train German artists in precision drawing and, by extension, precision thinking. Likely from a bibliographic reference, now long forgotten. I seem to recall ordering The Painter's Manual from British library, in 1993. As such, tiling forms but a small part of the book, in Book II, but nonetheless is of decided interest, especially with my interest in pentagon tilings, Dürer's work being the first known representation. As such, the book was briefly studied of the day (1993), but with other aspects being of lesser direct interest, was effectively put aside. As I recall, I was slightly disappointed with it, with more on tiling being expected. However, upon reading (June 2019) Noam Andrews’ 2016 paper, ‘Albrecht Dürer personal Underweysung der Messung’, my interest was once again piqued, upon finding that in his own first edition copy he made a series of corrections, and with further tilings. These are available in the digital collections of the German Bayerische Staatsbibliothek: However, the tilings are relatively minor, really only of interest due to the historical aspect. There are no further pentagon tilings.
Dye, Daniel Sheets. The introduction states that
these are designs that were not included in his earlier book 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.
————. This apparently first appeared
in 1937 titled as The
above is stated by Peter Hilton and Jean
Pederson of a reprint of
Eastaway, Robert, editor. A compilation from the pages
of New
Eastaway, Rob and John Haigh.
Eckler, Ross. 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. 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:
Edwards, Cyril. Although of repeat patterns and symmetry there is nothing of any real interest. Egleston, T. ‘Diagrams to illustrate the lectures on crystallography, delivered at the School of mines of Columbia college.’ Second Edition New York: School of Mines, Columbia College, 1872. Available on Hathitrust (7 January 2020) Of a Donald G. Wood reference (Space Enclosure Systems). Examined thumbnails (in the hope of pentagon tiling). Replete with crystal diagrams, but no tiling. Elffers, Joost. Translated by R. J. Hollingdale. Small format paperback, c. 200 pp. Perhaps more of a collaboration than the single author given suggests, with a Introduction (Jost Elffers with Erik van Grieken). History (by Jan van der Waals) pp. 9-27, and bibliography by (Jan van der Waals), pp. 29-31 pp. 123-124, an essay ‘Counting and Classifying Tangrams’ (by Michel Dekking with Jaap Goudsmit). Gives a most interesting and useful tangram history. Then gives a series of tangram diagrams without further commentary. Of general geometrical interest, nothing more. Quite what the background of Elffers is went unresolved.
Elffers, Joost and Michael Schuyt. A boxed set of tangrams and book.
Elliot, Marion.
El-Said, Issam; Ayse Parman. Many references to ‘tomb towers’ re Carol Biers’ interest. Elwes, Richard. 'Back to basics', and of its type most impressive, one of the better (if not one of the best) books. No tessellation.
Engel, Peter.
Ernst, Bruno. A major work on Escher, one of the ‘core value’ books; Indispensable! However, of note is just how little tessellation there is! The book is primarily on spatial structures. And what little there is, this is subsumed by the above premise.
————. Popular account.
————. 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
Escher, M. C. 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. 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.
————. Very large format book, 64 pp. In addition to the 29 Master Prints (by and large a fair description, given the inclusion of Day and Night and Sky and Water I, although no Verbum), both tessellation and others, the book includes an essay by Escher, 'On Being a Graphic Artist' and with commentaries on the prints, mostly by Escher, and additionally, in most a most minor way, by C. H. A. Broos, J. L. Locher, Bruno Ernst and H. S. M. Coxeter. However, none of this text appears to be original; it appearing in other sources, as according to the book. According to a reference on an old ring (cardboard) binder cover, I first saw this in Grimsby central library on 18 July 1992, but have since completely forgotten about this! Whether this was as on the shelves or was ordered I do not recall. Whatever, it was not significant in that no new studies arose from this.
Espy, Willard R. Although not strictly mathematical per se, being of word play, of interest to the mathematical mind, and so hence included here.
Falletta, Nicholas. The 1983 edition has a front
cover picture (among others) of Escher’s
Falkener, Edward.
Farnworth, Warren. Although not strictly on mathematics, included as it was studied among my early’ mathematical’ studies of 1987.
Farrell, Margaret A. (ed). 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 Has
Fathauer, Robert. Designing and Drawing Tessellations. Tessellations (Fathauer’s own company). 2008 (18 July 2009) First, I consider the title a little misleading, given that the premise is overwhelmingly one of creating, or of studies leading up to, of Escher-like tessellations, rather than generic tessellations per se as the title would otherwise suggest. Be that as it may, pleasingly, this is one of the few books to broach the topic of Escher-like tessellations in depth, and so is warmly welcomed, although I have various issues in places. As a generalised statement, the advice given by Fathauer is very good indeed, with many useful hints and tips as to the ways and means of creating Escher-like motifs. Although primarily aimed at a school-age level (12-16), anyone with an interest in creating Escher-like tessellations will find it advantageous, as it broadly addresses the all-important understanding of the underlying issues concerning the creation of life-like motif, of which this aspect is generally disregarded. Very few books concern themselves with this matter, even in passing, and of which lies at the crux of the problem of designing high-quality motifs, and so this aspect in particular is warmly welcomed. As such, one could argue that Chapters 1-4 of history and background matters, could very well be excluded on the grounds of familiarity, as previous books have covered the same ground. Still, for an easy, and convenient, ‘basics to hand’ covering of such matters, there is nothing to fault here. However, for those familiar with such matters, the book only really begins much later, with Chapter 5, this concerning the Escher-like aspect, with a series of tips on drawing and designing. Chapter 6 then gives a series of techniques, in effect attempts at improving upon the initial tessellation. Chapters 7-11 are concerned by more specific matters, with tessellations based on specific tiles that frequently occur. Broadly, upon the reader having absorbed each chapter, a series of activities are then given, suitable for the above age range. The whole book is in black and white, without colour and without Escher’s works. Escher references: Preface, pp. 1, 5, 7, 42, 47-51, 54-56, 66, 69, 71, 89, 93, 102, 129, 137, and 140. Note that these are mostly in passing, with only p. 5 of a true discussion. Note also that there are no pictures of his works. Cairo tiling references: P. 2, with a brief discussion, and p. 27. Also see my review of the book for a more detailed, specific analysis. Féblien, André. From a reference in The Sense of Order, by Gombrich. Tilings as such form a small part of the book, as glass panels. As occasioned by a revisit to Gombrich, of ongoing Michio Kubo interest, of which a plate from the book precedes that page. The book has * plates of tiling. Of historical interest, of innovation, albeit nothing truly outstanding. Available on the Internet Archive. Fellows, Miranda. 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. 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,
Feravolo, Rocco. Juvenile.
Ferris, Timothy (ed.) 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. 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
Field, Michael and Martin
Golubitsky. 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. Also see her article on ‘Kepler’s star polyhedra’.
Field, June. 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. 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, ————. Geometric Patterns from Islamic Art & Architecture. Tarquin Publications 1998 (First edition). Small format paperback, 63 pp. Downloaded from Internet Archive 31 December 2019 Very nice indeed! Primarily an image book, without pretence as to overt mathematics, with captions/text likely kept in the background. Of especial note: Whirling kites/Pythagoras tiling pp. 8-9 Breath of Compassionate pattern pp. 22-23 Bow tie tiling p. 40, at Brighton Museum and Art Gallery, of which I was unaware of! Other titles include: Geometric Patterns in Churches and Cathedrals, Geometric Patterns from Tiles and Brickwork, Geometric Patterns from Roman Mosaics: and How to Draw Them, Geometric Patterns for Patchwork Quilts Amazon: I have written six books on geometric patterns which are used by many people as a source of creative design in subjects as diverse as embroidery, patio paving, knitwear and quilt making. I also published and illustrated an anthology of poems about mice - I Think Mice are Rather Nice (Triplecat). I have also illustrated two books by my partner, the author Roderick Grant, Clap Hands for the Singing Molecatcher (Triplecat & Birlinn editions) and Strathalder - A Highland Estate (Triplecat & Birlinn editions). ————. Fletcher, David and Joseph Ibbotson. 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. Addison–Wesley Publishers Limited 1971 (3 September 2006). Juvenile. No real interest, primary maths. Symmetry pp. 50-54, no tessellation.
Fletcher, Alan. 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
Ford, Karin (translator) and Janet Wilson, editor. English
Language version. 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. 2. 3 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? 7. 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. 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. 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’’.
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. Juvenile.
Foster, Richard. A general account of the pavement. Chapter 6, pp. 111-130 concerns the aspect most of interest, from a geometrician point of view.
.From a reference in Bradley. A little disappointing,
in that tiling is only mentioned briefly pp. 363-371 on the PDF numbering. ————. From a reference in MacMahon. Strictly number recreations, of which although of
interest again disappointing, as I was hoping for tiling.Franke, Herbert W. 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 a loose parquet deformation nature; op art by A. Michael Noll, p. 67. Francis, Daryl. Freaker, Daniel and Alan Parsons. Series consultant Harry
Smith. For 11-16 age children. Features my bird and fish tessellation, p. 85. The text is Freaker and Parsons' own, of which I do not entirely agree with .
Freeman, Mae and Ira Freeman. 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.
Freese, Ernest Irving. From a link on Greg Frederickson’s update page, viewed (but not downloaded) at The Hathi Trust. As the title suggests, on perspective, with no foreshadowing of his work in geometric dissections, or anything on tiling per se.
Frederickson, Greg N. An absolute delight! Highlight
after highlight, too many to list here, although I am merely an ‘interested
bystander’ in the field. 24 chapters and an excellent bibliography. Speculations
as to who ‘A. E. Hill’ was, pp. 157-158, 290-291. Has many interesting brief
biographies of the main people in the field, past and present, including
Dudeney, p. 81. 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,
————. 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.
————. 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’).
————. (2 February 2018) At last, after no less than 60 years, Freese’s work is shown in its entirety!
————. ‘Hugo Hadwiger’s influence on geometric dissections with
special properties’.
Freebury, H. A.
French, P. Slim volume paperback, 39 pp. Juvenile, Junior, 8-11 years. Part of the 13-book series on the title ‘Exploring Mathematics’, by P. French and R. J. Rickard, under the general editor J. B. Palframan. Gives compass construction nets and brief history. although not explicitly stated for children, it is clear that this is the indeed the intended audience. Too simplistic to be of any use.
Friedhoff, Richard Mark and William Benzon. 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. 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, Further to the book, I happened to notice on the dust jacket the following intriguing quote:
Upon following up with him (mail, February 2017), he told me:
Therefore, it wasn’t a ‘special interest’ after all, but rather just a passing interest! But at least I know now.
Fuller, Buckminster R. Small format paperback, 416 pp. Text heavy. The cover has sphere packing diagrams, which my have attracted my attention. I simply don’t have the time to read this. It may come in useful for reference purposes. Chapter 3, Prevailing Conditions in the Arts’, on geometry, is the only aspect of direct interest. I read somewhere (Coxeter?) that Fuller was somewhat crankish (or overstated) in many ways. Whatever, the book was never studied per se.
Gale, Howard et al.
Gardiner, Anthony. Popular account from an academic, 153 pp. Not in possession, saw at Grant Thorald library on 15 September 1989 and made a minor study of that date on a shared paper of A. Racinet and Michele Byam of 10 and 17 January 1989 respectively. The book has long been deleted from stock, and ideally I would obtain again, if only to aid in a review. However, even of the lowest price on Amazon I am not planning on doing so. Pages studied 49, of circle packing and 73, of indeterminate means. Gardiner is a notable mathematician, with 15 books to his name; possibly this was the first. https://books.google.co.uk/books?id=tdO5-P4nRlIC&pg=PA49&source=gbs_toc_r&cad=4#v=onepage&q&f=false See Chapter 11, ‘Circles and Spheres’, pp. 49-51. and Chapter 16 Polygons, pp. 71-74. although ostensibly Chapter 11 is on circle packing, this is not so, or at least as seen at first impression such a fitting circles into a square. Rather the premise is of fitting the largest circles inside the central part hole of each configuration.
Gardner, Martin. 1. First, regarding the listing
of columns in Gardner’s compilations in books below, the entries in bold are of
extra special interest, primarily of tiling matters, although drawing hard and
fast lines is an invidious task at times. Quite simply his collection is
indispensable! However, annoying, and infuriatingly, these do not always reflect the original title and so correlating like articles is not a straightforward 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 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. 1 The Five
Platonic Solids, 2 Tetraflexagons, Of note is the Dudeney reference, of June 1958.
————. 3. (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, Of core interest: 17 H.S.M. Coxeter, with use of Escher's works: Horseman, Two Birds, Verbum
————. 4. 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 expecting other articles with the Dr Matrix columns, as
with other books in which an initial
title is insinuated. I have the second edition,
————. 5. 1 The Paradox of
the Unexpected Hanging, 2 Knots and Borromean Rings, 3 The Transcendental
Number e, Of most interest: Geometric Dissections, pp. 43-51 and Rep-tiles Replicating Figures on the Plane, pp. 222-233
————. 6. 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. 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. 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 is on MacMahon.
————. 9. 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. 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. 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 ————. 12 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, Of note is that this highlighted
contains 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. 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. 1 White, Brown and Fractal Music, 2 The Tinkly Temple Bells, 3
Mathematical Zoo, 4 Charles Sanders Peirce, 5 Twisted Prismatic Rings, 6 is on MacMahon and his cube puzzles.
————. 15. 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,
————. (editor.) Typical Loyd fayre.
————. (editor)
————. (editor)
————. Many aspects of interest (albeit largely outside of tessellation), too numerous to list. Especially see Chapter 4, Magic, of a wordplay nature.
————. (5 June 2013)
————. Popular account. Of note is Thomas Jefferson’s wheel cipher invention, p. 59.
————.
Gardner, Martin. Mostly philosophical speculations. Pentominoes pp. 92-93.
————.
————. Juvenile.
————. Pleasant coffee time reading.
Gives a good story of the great man in the round. A few snippets that I was
unaware of: his association with Salvador Dali. No Escher, perhaps
surprisingly. Mathematically, of most interest is Chapter 15, pp. 134-149, with
his association with
Garfunkel, Solomon. 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. 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.
Gerston, Judith (Series Editor) 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 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. 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. 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. Occasional Escher illustrations; 55-?
Gibson, Walter B. Although of a science premise of a children’s book, is included here as it has a small chapter on recreational mathematics: ‘Geometrix (sic) ‘Tricks Involving Geometrical Principles’, pp. 107-114. Included are Mobius strips and lost line, and Hooper’s cut. (Hooper is mentioned in the introduction).
Gill, George; publisher. (Author and date published oddly not
stated; c. 1900?). 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. 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. 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. Textbook,12-year- old target audience. Escher's swan outline used p. 49, unaccredited. Pattern, tessellation pp. 115, 117, 197-198 barely worth mentioning.
Glenn, William H. and Donovan A. Johnson. Small format hardback, 48 pp. Volume 4 of a 17-book series (none ostensibly on tessellation) of what is clearly intended for juvenile audience, although not stated as such. Without a doubt, readable, and ideally I would re-read, as for me at least it gives a splendid introduction to the Pythagoras Theorem, with numerous illustrations, although at times the mathematics is beyond me (and to an extent of interest too). Obtained in conjunction with volume 3, at a sale.
————. Juvenile, advanced.
Gleick, James.
Goldberg, Kenneth P. 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. Of very limited interest. Chapter 5, Networks and maps (topology) pp. 241-268.
Golomb, Solomon W. The bible of polyominoes; not that I’ve done much with it! Gombrich, E. H. The Story of Art. First Published 1950. 1972 Phaidon Press (9 October 2005) 498 pp. Gombrich, a noted art historian, has written many landmark books, including some of direct interest as to mathematics and Escher, of which it is thus not always easy to recall specifics. Therefore, I include 'all' here, even though not all bear any relation to mathematics and Escher, as indeed this is an instance. I checked the contents and index for any possible direct interest, of which there is essentially nothing. Much time could be wasted upon a casual browse through so many pages, and so I thus refrain from further investigation. ————. I can’t remember if I have this; perhaps I am confusing it with other books by Gombrich.
————. 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
————. Has occasional tessellations aspects, but this book continually flatters to deceive; it’s more of ornament in the broader sense than tessellation. Many aspects of interest. Has Escher boat and fish p. 89, Escher-like tessellation by an unknown Japanese, Michio Kubo, dated 1968 on p. 91. Frequent occurrence is the term ‘counterchange’ applied to any black and white tilings. I much prefer my own usage! The book has an excellent bibliography, with many books not commonly mentioned, most of which are worthy of following up. Gombrich is seemingly the popularizes, following up Stuart Durant (the circumstances of which is not detailed), of Douat’s Truchet tiling follow-up, pp.70-72.
Goodfellow, Caroline. A most pleasing scholarly approach, of a popular level. 128 pages. Of most interest is Chapter 7 ‘The Early Jigsaw’, pp. 110-117. Other chapters remain of interest, indirectly. Previously, I was unaware of Goodfellow. I see that she has written a variety of bygone games, dolls, toys type books, and of which I see that she was previously curator of dolls and toys at the Victoria and Albert Museum, and a member of Board Game Studies, an international society of experts on board games, a body of which, again, I was unfamiliar! Likely now that I am familiar with her name I will chance upon it upon game book reading.
Gorini, Catherine A. 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. Tessellation barely mentioned; just one line.
Green, Patrick. 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. 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.). Schattsneider
reference in 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.
Gregory, Richard L. Small format paperback.
Gribbin, John and Mary Gribbin. On numbers in science, rather than a mathematics book per se. Popular account. Occasional browse. P. 68 explains why toadstools have long stalks, the reasons of which I didn’t know before!
Grünbaum, B. and G. C. Shephard. The bible of tiling and mind boggling in its depth! Indispensable, although much is way too advanced for me. Largely, indeed overwhelmingly, academic, but still accessible on occasion. Cairo-esque p. 480, as part of the 24 polygonal isohedral types of proper tilings by pentagons. And much more beside!
Greer, A. Textbook. Tessellation pp. 297-300, very basic, barely worth mentioning.
. (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.
A weighty tome, of 1093 pages! Minor reference to
tessellation, p. 395 (albeit with poor quality diagrams) and Escher, p. 375.
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). 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 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).
Hambidge, Jay. 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. Hagen, Victor W von. The Roads That Led To Rome. Weidenfeld and Nicolson, 1967 (15 June 2019) Of pavement interest. A dedicated, authoritative account, 288 pp. Very nice indeed, of which a re-read would be ideal, given that much here was new to me. Has references to Ostia, but no pictures of the ‘gorseciki’ paving (I forget where I first became aware of this) Wikipedia: Victor Wolfgang von Hagen (St-Louis, Missouri, United States, February 29, 1908 – Italy, March 8, 1985) was an American explorer, archaeological historian, anthropologist, and travel writer who traveled in South America with his wife (Christine, later Sylvia). Mainly between 1940 and 1965, he published a large number of widely acclaimed books about the ancient people of the Inca, Maya, and Aztecs. Hanby, G. A.
Hand, William. ‘Scientific Mysticism’ in Use of Escher's print Hann, Michael A. and Briony G. Thomas. Patterns of Culture: Decorative Weaving Techniques. No. 36 in the Ars Textrina series, published in association with the University of Leeds International Textiles Archive (ULITA) as an accompaniment to the exhibition ‘Patterns of Culture - Decorative Weaving Techniques’. Foreword by D. Holdcroft. 80 pp. (25 June 2019) PDF Hann and Thomas have written many books/monographs together. Of weave interest. Skimmed read the PDF. Herringbone in Cairo, 4 BCE, p. 47. To what extent there is original research here is unclear. Relatively sparsely illustrated. No houndstooth. A detailed bibliography. Hannas, Linda (Introduction). 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:
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.
————. 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 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 http://www.opticalillusioncollection.com/2013_11_01_archive.html shows a later version of this, of 1884.
————. 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 Brothers puzzle ‘Society Dissected Picture Puzzle’ label, p. 18, although this does not appear to have been captioned or discussed. Also has ‘Before and after Marriage’ of 1789, p.11.
Harbin, Robert. The first of a three-book series, all of a like nature, with a brief introductory discussion of a few pages, followed by diagrammatic instructions. Only of minor interest, in passing, and not studied as such. As such, there is nothing here overtly mathematical, but I include here nonetheless, as paper folding can loosely be regarded as ‘mathematical’ in nature.
————. As detailed above.
————. As detailed above.
Hargittai, István; Hargittai, Magdolna. 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. Harpe, Pierre de la. Cairo tiling page 232, likely taken from George Martin’s work, given that it is the same ‘unusual’ configuration. c. late 2011? Harris, Ella & Caroline Christin (eds). 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.
Harrison, E. P. Scottish Estate Tweeds. Johnstons of Elgin, First Edition, 1995 (14 December 2020) Undoubtedly of the utmost importance. Hatton, Richard G. 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. Textbook.
Heesch, H. and O. Kienzle. 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 Schattschneider. Schattschneider, 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. Heesch, Heinrich. ————. Hemmings, Ray and Dick Tahta. Popular account of infinity, perhaps of a school-age audience, 96 pages. Oddly, the book does not have a contents
or introduction, or indeed, any structure at all! Escher’s Henderson, P. 'Functional geometry'. In Conference Record of the 1982 ACM Symposium on Lisp and Functional Programming, D.P. Friedman and D.S. Wise (Eds.). Pittsburgh, Pennsylvania, ACM Press, 1982, pp. 179–187. (2020) On aspects of Square Limit procedures. Most impressive. See http://www.ecs.soton.ac.uk/~ph/funcgeo.pdf. Hendler, Muncie.
Various tessellations, of 46 plates, in outline form. Of no consequence, being unstructured. Would appear to be intended as a child’s colouring-in book. Trivial.
Hendricks, Gordon. A minor study, of 9 and 23
August 1988, of an indirect manner of Escher-like tessellation, in which I
studied various animal’s outlines, as with this book, featuring horses, of a
five-sheet study. However, this type of study is no longer active, and of which
my interest essentially peaked and ended in 1988. The study, such as it was,
consisting of photocopying horse motion photographs of interest and then
assembling for easier viewing.
Heritage, R. Has minor tessellation, with a novel design method, not fully understood, and two Escher-like tessellations of a cat’s head with gaps and a fish? showing no understanding of the issues. Much to my annoyance, I cannot now find details of this book online, at Bookfinder, or elsewhere. Likely this was a primary or secondary school oriented. Hessemer, Friedrich Maximilian. Arabische und Alt-Italianische Bau-Verzierungen. Berlin, G. Reimer, 1842. Translated: 'Arabic and Old Italian Construction Embellishments'. (2013). Has many plates of decided interest. Especially see fused pentagon. First drawn to my attention by Pail Tucker, 2013. Available on Internet Archive. Heyden Van der, A. 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 discernible, 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. 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. 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! Also see Abbas, where this is named ‘Khatem Sulemanii’.
Highland,
Ester Harris. Juvenile, with a leaning towards historic aspects. Minor recreational aspects: Three utilities problem, map colouring theorem, no tiling.
Hilbert,
D. and S. Cohn-Vossen. 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. The content is now hopelessly dated, 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. 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.
————.
Hitchcock, Henry-Russell. World Architecture: An illustrated History. Bookplan, 1960. Oversize (22 June 2019) The subject is decidedly peripheral to my interests, but has occasional tiling. The text is by a gathering of experts. Hocking, Martyn. Tiling. Crescent Books, 1994. (9 November 2019) Wholly on the practical aspect of tiling, rather than the mathematics. It contains much useful advice, such as starting a tiling from the centre; intuitively, I would have begun from the side! And other useful hints and tips too, which I do not list here. As such, I have neglected this aspect of tiling, of which it only became of interest in 2019, upon a general side interest as tiles per se arising from the Cairo tiling studies as floors and wall tiles. Small format, 48 pp. hardback. Hoffa, Alan; Koss, Roberta. Tessellations pp. 242, 247, 253, 404-415. All inconsequential. 16-year-age.
Hoffman, Paul. Accessible account of Erdos’ life.
Hofstadter, Douglas R. 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! As such, I do not believe, that, unlike other Escher references, this was studied in any way.
————. Upon researching for parquet
deformation, as I do at random, in 2016 I stumbled across the work of David
Oleson, in which by circuitous means I found was featured in Hofstadter’s book.
This was a total surprise; I was under the impression that this was a simple
facsimile replication of his columns in
————. 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. and Pan Books Limited, 1967 paperback (7 March 1993 hardback; 16 April 1995 paperback) Small format paperback, of 649 pages! From the title, seemingly of a popular level, although still notably advanced for a general readership. Liberally illustrated. Lots of equations. The approach is indeed thorough, but largely beyond my interests and understanding. There may indeed be some aspects of interest, but finding these in such a lengthy book is not easy. Nothing really recreational, despite the title. No tessellation, polyhedra, Escher. Pressures of time forbids a re-read. The 1967 edition is described as ‘extensively revised with additional material and completely re-illustrated’.
————. Oversize, Juvenile.
Holden, Alan. Delightful, a popular account, readily accessible, from the basics on onwards.
Holderness, Jean. Textbook. Tessellation pp. 315-316, simple, barely worth mentioning.
Holiday, Ensor. Juvenile colouring book on tilings, of insignificant worth detailing here. A major drawback is that it lacks an index, making finding references awkward.
Hollands,
Roy. Tessellation p. 151, inconsequential.
Holme, Audun. Academic in tone, of a chance finding at a bargain price, and so bought. Oddly for a Springer book, riddled with typos and minor errors in English, likely due to the translation from the author’s native Norwegian to English. Overwhelmingly too advanced for me, albeit with occasional recreational aspects, along with readable histories that may be referred to as and when required. Minor referral to tessellations, of Archimedean pp. 233-239, and symmetry of plane ornaments p. 445.
Holt, Michael and Ronald Ridout. Illustrated by Peter
Edwards. Small format paperback, 142 pp. Usual introductory puzzle fare of all types, stated as ‘something for all the family’. The title is misleading; it’s a standard size paperback! Stated as a compilation of puzzles old and new, although of a scan I do not see anything new here. 153 puzzles with answers, but is not listed as such as contents, which is not given. Has Escher-inspired Relativity and Penrose staircase front and cover. No tessellation. In short, just a ‘fun book’ on puzzles, and there’s nothing wrong with that, and not intended to be for scholarly reference. One of many of its type.
Holt, Michael. A small format hardback, of just 99 pp. New maths subjects, with sets etc, in a recreational style aimed at the parent with a child. Various aspects of recreational maths of mild interest, but nothing more. No tessellation. Wikipedia: Michael Holt (born 1929) is a UK author of puzzle and quiz books for children, including several Doctor Who related quiz books and Crisis In Space in the Make Your Own Adventure with Doctor Who series. He was also the co-author of Puffin Books' Big Book of Puzzles series. He taught mathematics and geometry in London schools in the 1960s and 1970s.
————. From
a reference in Schattschneider and Locher. A small format paperback, of just 96
pp, of six chapters, of a popular level. Escher frontispiece, pp. 42, 46,
49-50, 77-78, 83. Most of the Escher references are in passing only, and in
when ‘in detail’ are brief. Illustrated with
Hooper, Alfred. Historical account. Newton, Leibniz, Gauss. Some mathematics beyond me.
Hooper, W.
Hopkins, C. H. No tessellation.
Hornung, Clarence P. 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.
Huberich, Paul G. Small format (square) paperback, American, 128 pp. The cover states ‘Methods used by the world’s foremost experts. Adapted for home study’. Gives guidance on arithmetic, some of which I have concerns with. p. 3 Arabic number beginning. Some seem decidedly obscure, beyond reason. e.g p. 21, to multiply any number by 16 2/3. The merits of the procedures given I leave to others. Date stamping has faded to point of illegibility. c. 1998? Also has other mathematical aspects, perhaps peripheral to the title. In short, of no practical benefit..
Huff, Darrell. Popular small format paperback account of statistics. However, of limited interest in the extreme, as I am not really interested in the subject. Lacks an index, which would help to find terms as given on the back cover. The seemingly basic ‘samples’ and ‘errors’ subcategories were unfamiliar to me.
Irving, Washington. Although not strictly a maths book per se, included for its tiling aspect.
Isenberg, Cyril. Soap Film Experiments with Kubic (sic] Bubbles. 'Manufacturer’s Guide Booklet' (no ISBN), not dated. (13 July 1995) Juvenile. Obtained at the height of my interest in soap film bubbles (1995), of which although I still have an interest, I have moved away from. Booklet, of 13 pp, from a self-assembled kit, for school children, to make two sets of four frameworks (tetrahedron, cube, prism and octahedron) and two plastic plates with joiners to view film in two dimensions. Begins with a historical discussion of Joseph Plateau, then advice on the assembly of the kit, and then references and further reading. Although not dated as such the back cover gives copyright ‘Advanced Educational Toys, 1974’. They are Knotts Lane, Canterbury (of Isenberg’s city). Wikipedia Cyril Isenberg MBE is an English physicist at the University of Kent, where he is an Honorary Lecturer. Isenberg is known for pioneering the analog computing possibilities of soap bubbles; in 2012, his 1976 article on the subject was one of a set of "classic articles" selected by American Scientist to celebrate their centennial. He has also frequently given physics lectures to schoolchildren and appeared in television shows, and is the organizer of the British Physics Olympiad. He is the author of books The Science of Soap Films and Soap Bubbles (Dover, 1978) and Physics Experiments and Projects for Students (with S. Chomet, Taylor & Francis, 1989 and 1996).
Jacobs, Harold R. 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.
————. 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, 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 next to worthless.
Compilation of popular puzzles in the style of
Dudeney. Usage is made of Hubert Phillips (Caliban) work. Next to nothing of a
geometrical nature.
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, Valerie (ed.). 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. 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. On polyhedra. Has five main sections, based on the platonic solids. Has many plates not commonly shown in books.
Jankel, Annabel and Rocky Morton. Good popular account of the early days of computer graphics. Of its time, and still of interest, albeit it has dated amazingly quickly. Snippets of direct interest include: p. 95, on Robert Abel, with an Escher-like image that from memory I saw in the Appendix in Art and Science; without it I doubt very much I would have noticed the association. This is from ‘Changing Pictures, TRW’, of which upon an initial look (2018) I could not find freely available. Islamic computer generated tiling as background p. 16. Posted on Broug Ateliers as to the earliest possible instance (although unlikely), with disappointing results (two insignificant comments!) Jarrow, Jastrow. Fact and Fable in Psychology. Houghton Mifflin Company, 1900. (Internet Download 21 April 2020) Of impossible/ambiguous figure interest, from a reference in Shuster. Of most interest is Chapter 5, ‘The Mind’s Eye’, with a profusion of illustrations. Of special interest is a houndstooth type diagram, p. 283.
Jaworski, John & Ian Stewart. Small format paperback, 125
pp. Typical children’s ‘fun’ paperback,
with 100 popular puzzles (with answers), albeit nothing more than a
compendium of well-known puzzles really. Lacks an introduction and index.
Escher-style illusions (no tessellations) are prominent, and indeed the cover
is a stylized version of Of
the authors, Stewart is too well known to document, although Jaworksi is
decidedly less so. Upon research, he appears
to have been Stewart’s colleague at Warwick University, and editor of
the university
Jeger, Max (edited by David Wheeler). Small format paperback, 143 pp. Part 1 of a five-book series. Translated from the German, with an English version by A.W. Diecke and A. G. Howson. Advanced in nature, way beyond my understanding. Reference is made to Escher and Terpstra in the bibliography. Oddly, there is no reference to Escher in the text (I checked each page, 2018). Tessellation of sorts pp. 42-43, but in the context of vectors. Of limited interest and use in the extreme. I have no plans to re-read.
Jenkins, Gerald and Wild, Anne.
————.
Jenkins, Gerald and Magdalen Bear. Nets to be assembled; disappointingly, no text is giving at all concerning the background to this.
————. A varied collection of polyhedra, to be assembled.
Jobbings, Andrew. Note 89.93. ‘Dissecting a triangle into
rectangles’. Popular account.
Johnson, Donovan A and William H. Glenn. 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.
————.
————.
Jones, Charles Booth-. Standard fare.
Jones, Christine. This looks like a museum booklet, of just 12 small pages, rather than a book per se.
Jones, Tim Glynne-. 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.
Jones, Lynn. 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:
Jones, Owen. 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
Judson, Horace Freeland. General Science. See Chapter 2, Pattern, in the broader sense.
Kappraff, Jay. 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 3 Parquet deformation pp. 190-194, within the chapter 5, Tilings with Polygons, albeit this merely excepted from Huff’s article (1983), as the author credits. ‘Consternation’ is shown.
Kasner, Edward and James Newman. From Wikipedia: Mathematics and the Imagination … rapidly became a best-seller and received several glowing reviews. Special publicity has been awarded it since it introduced the term googol for 10100, and googolplex for 10googol. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages. … According to I. Bernard Cohen, "it is the best account of modern mathematics that we have", and is "written in a graceful style, combining clarity of exposition with good humor". According to T. A. Ryan’s review, the book "is not as superficial as one might expect a book at the popular level to be. For instance, the description of the invention of the term googol... is a very serious attempt to show how misused is the term infinite when applied to large and finite numbers." By 1941 G. Waldo Dunnington could note the book had become a best-seller. "Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving." Edward Kasner (April 2, 1878 – January 7, 1955) was a prominent American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. James Roy Newman (1907–1966) was an American mathematician and mathematical historian. He was also a lawyer, practicing in the state of New York from 1929 to 1941. During and after World War II, he held several positions in the United States government, including Chief Intelligence Officer at the US Embassy in London, Special Assistant to the Undersecretary of War, and Counsel to the US Senate Committee on Atomic Energy. In the latter capacity, he helped to draft the Atomic Energy Act of 1946. He became a member of the board of editors for Scientific American beginning in 1948. Popular account. Eminently readable. Has many snippets of interest, although no tessellation. Uses the term parhexagon pp 14-16. Space-filling curves pp. 343-355. Chapter IV Assorted Geometries – Plane and Fancy predates Frederickson’s use of the term.
Kay, Keith. On optical illusions. Escher
tessellations
Keefe, John O’. and Phillip Rush. Advanced juvenile.
Kelsey, Kenneth and David King.
Kemp, Martin. A major work. As a broad statement, a series
on perspective, of notable 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 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. 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). 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. Available on-line from archive.org
Kepler Johannes.
Kim, Scott. Absolute delightful. Escher’s
Kirkby, David and Peter Patilla. A partial photocopy of relevant pages of interest. Very minor tessellation.
King, Elspeth. Small booklet, of just 12 pages. Gives a history. No mathematical tiles as such. Of general interest.
Kinsey, L. Christine; Theresa E. Moore. Tessellation pp. 57 onwards.
Klarner, David A. editor. A collection of articles in
honour of Martin Gardner, with tiling featuring prominently. Especially see:
Kline, Morris. 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!).
————. Of limited interest.
Kneale, Nicholas. 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). 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.
Knuth, Donald. Volume 1 Fundamental Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xx+650pp. ISBN 0-201-89683-4 Volume 3 Sorting and Searching, Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout. Grunbaum reference. High-end,
computer talk, way beyond my interest and understanding. Martin Gardner,
Kordemsky, Boris A. (edited by Martin Gardner) Wikipedia Boris A. Kordemsky (1907 – 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles. Kordemsky was born in Kiknur, Vyatka Governorate, Russian Empire. He received his Ph.D. in education in 1956 and taught mathematics at several Moscow colleges. Kraitchik, Maurice. Twelve chapters on various aspects of recreational mathematics, with most of note Chapter 8, pp. 193-213 on tilings, with: 1. on Geometric Recreations, 2. Mosaics, pp. 199-207. Also see 3. Mosaic on the Sphere, pp. 208-209. Simple tiling diagrams, and ways of tiling with various regular polygons in combination. Mention of MacMahon p. 53 as regards Bachet. The preface mentions a French edition of sorts. Kubo, Michio. Hidden Birds. Self Published, 1968 (29 November 2019) A scan of the book, kindly undertaken by Makiya Torigoe. The otherwise obscure title refers to the figure ground aspect of Kubo’s black and white tessellations, seen throughout the book. In essence a picture book, no text, or even captions! Kurajica, Stanislav. Rendgenska Difrakcija Na Prahu. HDKI/FKIT, 2020 (29 December 2020) = X-ray Diffraction Powder Uses (with my permission) my Birds and Fish tessellation, p. 46. Academic, in Croatian. The book is on X-ray diffraction, way beyond my understanding, and of which there is no other tiling as such. Only skimmed.
Laithwaite, Eric. Brief discussions on Mobius band, flexagons and polyominoes. pp. -31; 75-79.
————. 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.
Langdon, John. Delightful. Langdon can be described as a master of his craft. Escher pp. 170
Langdon, Nigel and Janet Cook. Juvenile. Usage is made of Escher’s Swans tessellation, p. 13, but without detail or credit!
Langdon, Nigel and
Charles Snape. Of note is a tessellation section, of an Islamic tiling, pentagons and Escher-like, not all of which I photocopied, with only p. 19 so copied.
Langdon, John.
Larcher, Jean. 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. 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. Popular account. Never played the game though! Got on general interest.
Last, Derick (ed.) Of interest is a Cairo pentagon-esque in combination with a kite, p. 5. Many computer drawn examples, badly dated. Tiling pp. 49-51, 54, the latter of Escher-like ‘gnomes’, by Richard Ladds.
Lanz, Sherlee. Trianglepoint. From Persian Pavilions to Op Art with One Stitch. The Viking Press 1976 (28 June 1998) From a reference in Grünbaum. All of a triangular premise. Has many pleasing tessellation aspects throughout. Of note a truncated houndstooth tiling, titled ‘snowcaps’ colour plate 29 and p. 96 where it is stated ‘woven shawl, nineteenth century, the Sandwich Islands’, which I have seen quoted elsewhere.
Lea, Derek. 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
Leapfrogs.
Leapfrogs. Some tessellation but treated in a lightweight manner. Written in conjunction with a series of posters produced by Leapfrogs.
Lemon, Don. 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. Lemmen, Hans van. 5000 Years of Tiles. British Museum Press 2013, 304 pp. (28 August 2019) Escher p. 252 (name check) and pp. 254-255, in Chapter 6, ‘The Century of Design’. A small paragraph on Escher, in the context of tile history, of his tile design made by De Porceleyne Fles in Delft. Illustrated with Swans. A good general history. Lewis, Donald J. Academic. Illustrated with Escher’s
prints: Cover, Preface,
Levy Joel? 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. Juvenile, but still of interest.
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. Popular account, from a physicist.
Licks, H. E. From a reference in Stegmann’s site. 15 puzzle pp. 20-21; magic squares pp. 39-43, geometric fallacies pp. 54-55, map colouring pp. 61-62, bees speculations pp. 91-99, 155 pages.
Liebeck, Pamela. Tessellation, pp. 118-119 (includes a fish of no great merit). Basic, as to be expected.
Lindgren, Harry. 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. 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). 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!
————. Another core value book, indispensable. Has five essays: The World of M. C. Escher, J. L. Locher; Escher: Science and Fiction, C. H. A Broos, Approaches to Infinity, M.C. Escher. Structural Sensation G. W .Locher, The Mathematical Implications of Escher’s Prints. H. S. M. Coxeter, and a catalogue of the more important prints. Includes a excellent selected three-page bibliography, pp. 57-59, with misspelling of Maas.
————. The book is described as:
‘This 1984 edition is published by Harry
N. Abrams Inc. New York. It is a concise edition of Abrams’ The World of M.C.
Escher, originally published in 1972…’. 151 pp as against 263 pp. Tihis concise
edition has only two of the five essays of the earlier book (‘The work of M.C.
Escher’ and ‘Approaches to Infinity’). It also lacks the ‘Selected Bibliography’
and ‘Exhibitions and Lectures’. Most of the plates are retained, albeit with
minor rearrangements. The colour plates remain the same. As such, I see little merit to this concise edition; there is nothing new here. indeed, with
Locher, P. and C. Nodine. ‘The Perceptual value of symmetry.
From a Craig Kaplan thesis reference.
Locke, John.
Lockwood, E. H. 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. Largely of an academic nature. ‘Indirect’ Cairo reference p. 88. Escher p. 4, Shells and Starfish, E42, Fish E41, p. 66 Lizards, E56. Shows a houndstooth design p. 90 (on a small piece on making automatic reproductions), and of which although claiming to be from the Sandwich Islands (clearly derived from Owen Jones' account, with plaited straw) is not strictly so. Rather, for unclear reasons, this is a variation, indeed interesting in itself, but is not directly based on the Jones diagram.
Lodding, Ken. ‘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. 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 Australia Puzzle p. 54.
Loeb, Arthur, L. 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.
————. 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. Of peripheral interest. The book has cut out nets to assemble, but not undertaken. Commentary is given as to the domes.
Love, Brian. 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. Although not a maths book per se, included as it has a picture of the Cairo tiling. Cairo tiling photo at the Old Cataract hotel pp. 8-9. However, this is only recognised with foreknowledge, as the picture is from afar that without cognizance of the tiling would otherwise pass unnoticed. The photographer credit is ‘The Image Bank, Kodansha Images’, but upon searching I could find no reference to the picture here.
Loyd, Sam [Jr]. As compiled by his son, Sam.
Impressive, even when due allowance is made for unaccredited borrowing from
Dudeney. However, the book is not without fault. Gardner states (in
Lukas, Edouard. 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. 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. 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
MacMahon, P. A. Most impressive. Has considerable tessellation interest. Cairo diagram (but obviously not attributed) page 101, the first (1921) recorded instance in a book or article? (Moore's patent predates this). The only possible precursor to this is Haag (1911), as the others in Schattschneider’s list i.e. Laves et al are all after 1921.
Madachy, Joseph S. First, note the title change
as above. Originally saw this (
Malone, Maggie. 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. Essentially an illustrative book, with any text at a premium. Note that the 1001 designs are not discussed individually.
Mallinson, Phillip R. Note that I have this as a PDF rather than a book. Cairo tiling p. 17.
Mankiewicz, Richard. Escher, pp. 6, p. 125 Circle Limit IV, p.129 Mobius Strip II .
Maor, Eli. 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. 365 pp. From a reference on an old cardboard ring binder with a Grimsby Central library reference. The reference also mentioned the similarity of a hexagon to the outline of France. I now (2018) do not recall anything from this book. As such, it was likely seen out of possible interest in and nothing more. Certainly, no studies have emanated from it. I am not actively going to pursue this.
————. A weighty tome of 468 pages. I have seen occasional references to this, although Escher and tessellation are mentioned essentially in passing, in regard of hyperbolic geometry, pp. 23, pp. 158-169, and bibliography. The nature of an electronic copy prevents a pleasant reading, of which I have looked at just the first few pages.
Marjoram, D. T. E. The only interest is in Chapter 10, Topology.
Holt, Michael and D. T. E. Marjoram. First seen, or at least recorded on a shared sheet of many different studies. E. H. Lockwood describes this as of CSE level, which book I saw is uncertain. A reference 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. No entries for ‘Tessellation’ or ‘Tiling’! Be that as it may, still a handy reference guide.
Martin, George E. 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. Advanced it is indeed, of
which despite claiming to be aimed at
McCann, Chris. 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.
McCleay, Heather.
McCloud, Scott. From a reference in Craig Kaplan’s thesis. Has many salient point indirectly as to Escher-like tessellation.
McCormack, Tony. On in situ paving (having previously seen his most informative and interesting website on paving). Mostly of background matters as to the intricacies of paving; as such, there is next to nothing on pattern in the broad sense. Of little to no interest mathematically.
McGary, Debi. NOT IN POSSESSION Although not a maths book, included as regards my cluster puzzle interest. Anne Williams reference. Six wood-themed cluster-type puzzles, with the veracity varying considerably, from true tessellation to considerable vacant regions. Her work is inconsequential. McGary is oddly anonymous on the web.
McGregor, Jim and Alan Watt. 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 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. Historical account. 18 Chapters. Of little direct interest.
McMorris, Penny. 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. ‘How to…’ book.
Meer, Ron van der. 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. ‘Ascending and Descending’ and ‘Relativity’, pp. 92-93. Minor text.
Meyer, Franz Sales. The book is rather of ornament in its many forms rather than tessellations. However, there are indeed tilings here, notably pp. 10-12, albeit simple, of an arbitrary nature without structure. Of note in particular is of plate 6, diagram 11. This can be seen to be the same tiling as of Pólya’s Do3 diagram, and so predates this. Also, pp. 279-280.
Michell, George. Oversize coffee table book. Purchased for a specific reason. Upon a (2018) reading of a 17th century Cairo tile Mughal jali reference in Simon Ray’s Islamic catalogue of 2016, in which this book, being the sole quoted reference, appears to be the source. However, I find that this is not so; it is not in the book! A major disappointment in this regard, to put it mildly. However, there is at least an interesting chapter on Geometry, pp. 68-107, that discusses tilings. Also see Jan Pieper and George Michell for more on jalis. Michell was a new name to me, although I see that upon a coincidental contemporary chance revisit to Craig Kaplan’s thesis he gets a sideways mention, p. 206, reference 98.
Midonick, Henrietta. Small format paperback, 416 pp. In four sections: Further Development, Algebraic Geometry and Calculus, Logic, Modern Algebra. Select text from existing works. 24 biographies on ‘the greats’. Most of this is way beyond my understanding. Largely accessible is Albrecht Durer, pp. 104-122. Useful for reference purposes, but nothing more. I have no plans to re-read.
Miller, Charles D., Vern E Heeren, John E. Hornsby, Jr. 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. ‘Cairo crossword’ puzzle, by ‘Croton’, from
Mirrow, Gregory. 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). 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. This book is one of a six-part
series from ‘Topics of Mathematics’,
three of which are by Mold ( Small, 32-page booklet, for children. Very accessible, with much of interest.
————. School age level, but still of interest. Shows dual Archimedean tiling, p. 25, which can be interpreted as Cairo. Also interesting fish tiling that has dual properties, possibly as a by-product of drawing, rather than purposefully so. Also of note, as regards Robert Ferréol’s interest in examples of Pavage de Diane, is p. 17, where there is a report of this as an in situ tiling ‘… on the floor of an old shop in Windsor’, with a side reference to Windsor Castle. Upon an initial look, this was not, unsurprisingly, found.
Montrose, Clifford. Small format paperback, of 90 pages. Stated of a variety of indoor games that you can play alone. Nothing of an overt geometrical nature. Includes: Solitaire pp. 16-19, The Wonderful Puzzle Fifteen pp. 41-43. One of many of its type, with no plans for a re-study.
Moon, Brian. 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.) Escher’s
Morgan, Bryan. Poplar account, from over 5,000 years to today. The discussion is in general terms, rather than focusing on specific individuals as an in-depth detail.
Morgan, W; Pickering, J. R. Textbook, typical of the day, with many problems in calculation, of little interest.
Morris, I. H. and Joseph
Husband. 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.
————.
————. 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.
————. 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.
————. Somewhat disarmingly here, p. 76, on the golden ratio propagates (or at least seems to imply) the ‘belly button’ myth.
————.
————. The Monty Hall Problem.
————. Sterling Publishing Co, Inc, New York, 2006
Moser, Koloman. Dover states that this: ‘is a
republication of all the plates included in the portfolio Historically significant, as
here are the
Mottershead,
Lorraine. 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
cover has an op art design apparently attributed to one Chris Belson. However,
he is not the designer! Carraher and Thurston in Of note is that Mottershead
shamefully appropriates (1963) Gettings’ diagrams in The first of two books of a like nature by Mottershead, although wide apart in chronology, namely of 1977 and 1985.
————. No Escher references or pictures. The book consists of 6 units, or chapters. As with Mottershead’s earlier book, this is very much in the same vein, of a recreational nature. however, here, as an observation, more on numbers, rather than symmetry matters of the other book. That said, there is indeed tilings here, and indeed, this was studied in 1987 (at Grimsby reference library).
Mott-Smith, Geoffrey. Has geometric dissections p.
————. Small format hardbook, 245
pages. In three parts: 1. Card Games, 2.
Board and Piece Games, and 3. Word Games and Pencil-and-Paper Games. The main
essence is on card games. Only of minor passing
interest, with nothing really in my field. Note that Mott-Smith was a geometric
dissection enthusiast, and is discussed in Frederickson,
Munari, Bruno. On design, rather than maths. Occasional mathematics. Note that Munari is an associate of Mari. ## Murchie, Guy. The Seven Mysteries of Life: An Exploration in Science & Philosophy. Houghton Mifflin Company. Originally published 1978. Part seen on Google Books. (21 April 2020)## P. 467 Cairo tiling in the context of pentagonal chicken wire. Unsurprisingly, the connection is not made. Found by chance upon Twitter responses with T. Sundra Row.Murphy, Lawrence R. 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. 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, unattributed, p. 200. This book has played a notable role in my early studies, in which in 1987 I studied it extensively. However, the ‘Escher-like’ tessellations by Murphy show a complete lack of understanding of the issues and are a veritable disaster!
Murphy, Patrick and Albert F. Kempf.
Nath, R. The subject of recent October
2018 interest due to a stated 17
Nasr, Seyyed Hossein. 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 convenience (although the book is economically available). Nasr is a prolific author, with 29 publications to his name (on the internet archive site), easily confused. However, my original book title reference is indeed as stated. Much of the book had been forgotten pending the download.
Necipoğlu, Gülru and Mohammad Al-Asad. The Topkapi Scroll: Geometry and Ornament in Islamic Architecture. Getty Research Institute, U.S. 1995. 384 pp (£621 cheapest copy!) Available as a free PDF on Getty site From a Peter Cromwell reference, and likely others. Synopsis Since few architectural drawings and no theoretical treatises on architecture remain from the pre-modern Islamic world, the Timurid pattern scroll in the collection of the Topkapi Palace Museum Library is a valuable source of information. This text provides an analysis of the scroll dating from the late 15th or early 16th century, and aims to throw light on the conceptualization, recording, and transmission of architectural design in the Islamic world between the 10th and 16th centuries. It compares the Islamic understanding of geometry with that found in medieval Western art. The scroll, with its 114 individual geometric patterns for wall surfaces and vaulting, is reproduced in this volume. A catalogue includes illustrations showing the underlying geometries, in the form of incised "dead" drawings, from which the individual patterns are generated. An essay by Mohammad al-Asad discusses the geometry of the "muqarnas" and demonstrates by means of CAD drawings how one of the scroll's patterns could be used to design a three-dimensional vault. Gülru Necipoğlu (born 1956 in Istanbul) is a Turkish-born American professor of Islamic Art at Harvard University. She been Aga Khan Professor of Islamic Art and Director of the Aga Khan Program of Islamic Architecture at the Department of History of Art and Architecture in Harvard University since 1993, where she earned her PhD in 1986. She specializes in the medieval and early modern periods, with a particular focus on the Mediterranean basin and the Eastern Islamic lands. She is the editor of Muqarnas: An Annual on the Visual Cultures of the Islamic World and Supplements to Muqarnas. Her books include Architecture, Ceremonial, and Power: The Topkapi Palace (1991); The Topkapi Scroll, Geometry and Ornament in Islamic Architecture (1995); and The Age of Sinan: Architectural Culture in the Ottoman Empire (2005). Her critical interests encompass many subjects, including methodological and historiographical issues in modern constructions of the field of Islamic art. Nelson, David et al. 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
Nelson, David (editor). Serious reference guide. Tessellation gets a brief mention, with two illustrations.
Newell, Peter S. Of note is the ambigram, p. 31
Newman, James A. (Newman also wrote a foreword
to
Nicolas, Alain. Delightful! Nicolas is a master of his craft. A must have for anyone interested in Escher-like tessellation.
Nichols, T. B. and Norman Keep. Of minor interest. Although of a geometric construction premise, of first principles, at least to begin with, there is indeed some patterns of interest. Fret patterns pp. 88-90, patterns based on squares pp. 90-91, patterns based on circles, pp. 92-93 patterns in circles pp. 94-95 and tracery, pp.196-199. I believe I first saw this book in 1987 (at the college library?) and loosely studied with some geometric constructions of the day. There is no tiling as such. Nisbet, Harry. Grammar of Textile Design. Scott, Greenwood & Son. First Edition 1906 276 pp. (seen). Second edition 1919, Third Edition 1927 (seen). (26 February, 8 March 2019) PDF Of an undoubted expert on the subject. Has a Cairo tile unit block, ‘linear zigzag weave’, p. 101 (first edition), but I don’t at all understand the correlation between supposed related diagrams. That said, although doubts remain, surely a Cairo tiling is intended. This is of obvious note as one of the earliest examples, namely that of 1906. The book was mentioned in Grünbaum and Shephard’s article ‘Satins and Twills’, but found independently! Nixon, J. T. Juvenile. Norgate, Martin. ‘Cutting Borders: Dissected Maps and the Origins of the Jigsaw Puzzle’. The Cartographic Journal. The World of Mapping Volume 44, 2007 - Issue 4 (May 2020) Jigsaw/John Splisbury reference. A valuable contribution to the debate on the originator of the jigsaw puzzle. Norgate categorically asserts this to Madame de Beaumont rather than Spilsbury. As a general statement, it is not always clear as to what is original research on Norgate’s part. However, although it repeats established knowledge in parts, I like this piece very much. Northrop, Eugene P. Largely popular account, of ten chapters with the last of a more advanced nature. Largely of paradoxes and fallacies, derived from stated sources, as detailed in the preface. Not tessellation as such, but of much related and other material of interest; of minor optical illusions, dissections, space-filling curves, Mobius band, four-colour theorem to name but few. The overall tenure is largely of an advanced nature, although the above is indeed of a popular level.
Nunn, G. 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 tessellations can be found on in the Appendix, p. 327, which is ‘typical teacher’ i.e. not idea!
O’Beirne, T. H. A collection of articles which
appeared in
Obermair, Gilbert. Small format hardback, 144 pp., 14 Chapters. Popular tricks with matchsticks, with answers. Gives a history of the match p. 7. P. 8 is interesting in that it shows how best to strike a match, in a counter intuitive way, not the more obvious lengthwise strike, but breadth! I had never even considered this! To what extent the puzzles are original is not readily detectable; certainly, there are no references or bibliography. Likely, they are a re-hash of existing material, given the historical account below. Makes for a mildly amusing coffee-time reading, but there is nothing of significance here. A brief history: From: Aims Education Foundation on 12/3/2005 Source: http://www.aimsedu.org/Puzzle/3to5/index.html In the 19th century matches
were first manufactured. Invented in 1827 by the British chemist John
Walker, matches soon replaced the tinderboxes that people had formerly used to
light fires. As matches grew in popularity and became ubiquitous
later in the 19th century, they spawned a new form of entertainment matchstick puzzles that became quite popular
when several match companies printed these puzzles on their boxes. Capitalizing
on this interest, publishers began to print books of match-stick puzzles. By
the turn of the 20th century, many people had developed a personal
repertoire of these puzzles and used them to challenge friends and
acquaintances. The toothpick puzzle presented here is modeled after these classical matchstick
puzzles.
O’Daffer, Phares G and Stanley R. Clemens. Chapter 4, p. 86-117 Patterns of Polygons: tessellations, albeit very basic in scope. Has Cairo tiling p. 95. Occasional usage of Escher’s prints: Day and Night p. 86-88, Horseman p. 114, Magic Mirror, p. 215. Oelsner, G. H. A Handbook of Weaves. The Macmillan Company 1915. Translated and Revised by Samuel S. Dale. 1875 illustrations 131 pp. PDF (2019) Of fabric interest. As to background matters, Oelsner was the director of the weaving school at Werdau, Germany. The translator has added a supplement. Referenced in Grünbaum and Shepherd’s 1980 Satins and Twills article. As such, the numerous illustrations are of an abstract nature. As such, no houndstooth or related material. Consequently, the book is of limited interest. Deemed not worthwhile to purchase. cs.arizona.edu has both the 1915 edition (the first?) and a dedicated extract of the diagrams, of which a houndstooth is to be found. WIF (weaving information file) number 44248.
Ogawa, Tohru, Koryo Miura, and Takashi Masunari. 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; Pamela McCracken; Loretta Fontaine; Bryce Bixby; Of interest: Analysis of Marcia P Sward Lobby Tiling by Teruhisa Sugimoto (Marjorie Rice tiling) Search of Convex Pentagonal Tiling with 5-valent Nodes by Teruhisa Sugimoto Oguro, Sabu. Fox Chapel Publishing, 2012 2014, 160pp. WANTED Note that this is one of those books that although ostensibly in print, are seemingly simply not available. O’Keefe, Michael and Bruce G. Hyde. Crystal Structures 1. Patterns & Symmetry. Mineralogical Society of America, 1996, 453 pp NOT SEEN IN FULL Of Cairo tiling interest, p. 207: The pattern is known as Cairo tiling, or MacMahon’s net and In Cairo (Egypt) the tiling is common for paved sidewalks… The second use of the term ‘MacMahon’s Net’ for the Cairo tiling, having previously been used by them in their 1980 paper, ‘Plane Nets in Crystal Chemistry’, but this time in addition with the Cairo association. However, this is very much an ‘unofficial’ description. Upon correspondence with him (2012): I suspect I got ‘Cairo tiling’ from Martin Gardner who wrote several articles on pentagon tilings. He is very reliable. As to ‘MacMahon's net’, I got the MacMahon reference from Cundy & Rollet….We are mainly interested in tilings on account of the nets (graphs) they carry. Possibly, and plausibly, this by MacMahon, of 1921, was the earliest known representation, and so in a sense it was indeed broadly justified, even though by 1980 the ‘Cairo tiling’ term was coming into popular use, although if so, it is now been left behind by my subsequent researches. Curiously, the term is used on the Cairo pentagonal tiling Wikipedia page. However, the page leaves much to be desired, including this designation. Toshikazu Sunada has also used this term. However, I do not like this at all; it seems a somewhat artificial, additional naming, and seems unnecessary. Better would simply to have credited MacMahon as the first known instance (at the time) but without naming it after him.
Oliver, June. 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. 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.
O’Shea, Donal. Semi-popular account.
Osler, Dorothy. 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. 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
Padamsee, Hasan S. P.132
Paling, D. Only of interest in a historical sense, as it was one of the earliest* books on tessellation (and maths per se) I studied, c. 1986. Tessellation pp. 272-272, with the ‘any triangle, quadrilateral will tile’ rule. * Have I mixed this up with the book immediately below?
Paling, D. and J. L. Fox. 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. Essential reading on the subject. History of
cluster puzzles (of the type as evinced by Escher’s
Pappas, Theoni. Gardeneresque.
————. Collection of popular mathematics, typically over a two-page spread, sometimes three pages. Tessellation pp. 120-122.
————.
————. A few good (brief) yarns, although apparently no original research per se, with the material seemingly taken from existing sources in the bibliography. In short, essentially cuts to the chase from other, more in-deth treatments.
Paraquin, Charles H. Juvenile. Usual repeats of established illusions.
Parsons, Richard. Textbook. Faryna-Paszkiewicz, Hanna and Zuzanna Fruba. Warszawskie gorseciki zanikajace (Translated: Warsaw’s Vanishing Corsets). Nisza Publishing House (in Polish) 2013, 336 pp. (13 August 2019) On 'gorseciki' (corset) tiles, of recent (July 2019) interest. Fantastic!
Pasztory, Esther. 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.
————. Popular account. Small format paperback, of mild general interest, but nothing of note as regards my specific interests.
Peak, David; Frame, Michael.
Pearce, Peter and Pearce, Susan. Non attributed Cairo tilings on page 35, and in the context of the Laves tilings, page 39.
Pearcy, J. F. F; Lewis, K. Juvenile. A bit like Mottershead, but for a younger age. Tessellations 14-15 (B1) reptiles 8-9 (B2).
Pedoe, D. Small format largely popular paperback,
160 pp. As such, although largely on popular subjects, there is very little of From Wikipedia. Dan Pedoe (29 October 1910, London – 27 October 1998, St Paul, Minnesota, USA 1]) was an English-born mathematician and geometer with a career spanning more than sixty years. In the course of his life he wrote approximately fifty research and expository papers in geometry. He is also the author of various core books on mathematics and geometry some of which have remained in print for decades and been translated into several languages. These books include the three-volume Methods of Algebraic Geometry (which he wrote in collaboration with W. V. D. Hodge), The Gentle Art of Mathematics, Circles: A Mathematical View, Geometry and the Visual Arts and most recently Japanese Temple Geometry Problems: San Gaku (with Hidetoshi Fukagawa).
————.
Peitgen, Heinz-Otto et al. Volume 1 of a two-volume series. As such, given their content I am at a loss to explain why I purposefully pursued these books (ordered from Claire Publications). Although I have a mild interest in fractals, this is really only in passing, as the subject quickly becomes highly technical, way beyond my understanding. I have a dim memory of them being on offer, at half price, and so it seems that this was enough to induce me. Whatever, the premise of the books are for the classroom, with the six authors (Peitgen, Jürgens, Saupe, Maletsky, Perciante, Yunker) leading lights in their field. Volume I (128 pp) is notably easier than volume 2 (187 pp). Even so, still much is obscure in the first. A graphics calculator seems a prerequisite. Unsurprisingly, no tessellation or Escher. Simply stated, an ‘unwise’ purchase. I have no plans to re-read.
Peitgen, Heinz-Otto et al. As detailed above.
Penkith, F. E. 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. Mostly too advanced for me. Occasional
tessellation, of non-periodic tilings, and their background, pp. 172-178. Occasional
Escher references,
————. Weighty tome, of 457 pp. As to be expected by the tenure of the book, this is almost entirely beyond me, the only aspect that is vaguely understandable is a short discussion on tiling in the context of the ‘tiling problem’, in Chapter 1, ‘Consciousness and computations’, with two pages of polyomino diagrams, pp. 29-33, Robert Amman influenced. No Escher.
————. 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. ————. 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. Chapter 7, pages 200-212, ‘The Fivefold Way’, with Penrose tiles.
————. See ‘Paving the Plane’, pp. 83-86.
Petrie, Flinders W. M. Checked for Cairo pentagon – no reference.
————. Checked for Cairo pentagon – no reference.
Phillips, Peter, and Gillian Bunce. First saw in art school library, and duly studied, disproportionately so, the exact memories of which have long since faded. The premise is of using a computer for drawing tessellations.
Pick, J. B. (Compiler). Subtitled as ‘Outdoor, Covered Court, Gynnsuim and Indoor’. How to play 501 games Of game and puzzle interest. Five chapters, of (I) Full Dress, Outdoor Games, (II) Informal Outdoor Games, (III) Covered Court Games, (IV) Gymnasium Games, (V) Indoor Game, with many subchapters. Potted details, rules and history of games, not illustrated. Of most interest is (V) Indoor Games, with a subchapter on Board and Table Games, pp. 229-263. However, there is nothing overtly mathematical here. The background of Pick went unresolved.
Pickover, Clifford. (24 July 2016)
Pickover, Clifford. Dewdney’s ‘informal tesselation (sic) of Cats’ cluster puzzle picture. Not that he told me about this when we corresponded!
Pieper, Jan and George Michell, editors. From a reference in Craig Kaplan’s thesis, p. 206. A reference to Haresh Lalvani and Pattern regeneration, on jalis.
Pinto, Edward & Eva R. Non-mathematical interest, primarily of jigsaw history. Especially see plate 8, of a ‘treadle operated jigsaw, by W. Fenner, about 1760’.
Pipes, Alan. Has occasional Escher, with Pizzuto, J. J. and P. L. D'Alessandro. 101 Fabrics. Analyses and Textile Dictionary. New York: Textile Press, 1952 (8 April 2019). Viewed online at Hathitrust, seemingly not available as a PDF From a reference in Grünbaum (Satins and Twills article). The premise is of a illustration of a term (cashmere etc.) with a swatch, technical details and then dictionary entry at the end of the book. Popular account. Houndstooth p. 43 Glen Plaid p. 39. Note that no other terms I have studied are included, such as Shepherd’s Check, Border Tartan etc. Useful, convenient reference to the fabric terms in a generalised sense. Plichta, Peter.
Pohl, Victoria. Geometric string designs, in two and three dimensions. Ostensibly for children, 68 pp. No tessellation. As such, now, and for a considerable while, only of limited interest. For a while, amid my geometric studies of 1987, I was interested in such designs, and so likely with that in mind obtained the book by chance, from my visit to John Bibby in York, where I had to make a choice of ‘buy or lose’ at the the time, this of course predating the internet. Although of a popular geometric nature, if seen for the first time I would now not be so enthused, and certainly not at cost price! Further, unlike other books from Bibby, this was not studied in any way, and so this, even of 1994, reflects a realisation that this was not of direct interest. Be that as it may, it just may have been, and so in that sense the purchase was justifiable.
Polster, Burkard (with foreword by John Langdon). A prize in an Australian
tessellation contest that I won run by Polster. Very nice indeed, in the same spirit
as with John Langdon’s
Pólya, G. Of limited interest.
Price, Jeffrey. Gift of Jeffrey Price. Much of interest, with many previously unpublished materials and Price’s own insights concerning Escher.
Priestly, J. B.
Pye, David.
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.
Racinet, A. Essentially of ornament rather than tessellations. Although of a tome of major undertaking, it is of little direct interest as regards tessellation. Pages of interest, with tessellations, include 77, 123, 129, 135 and 149, albeit there is nothing in the way of innovation. Time constraints forbid an considered examination of the text. The two red and blue diagrams of Egyptian tilings, p. 77 are repeated in**. p. 129 and 135 are Arabic patterns. Note that this book was studied briefly, almost derisorily, on 10 January 1989, albeit seemingly of just a single sheet (amid non-related studies) and is of no consequence. Fom Dover: Presents one
hundred plates in color, comprising upwards of two thousand specimens of the
various styles of ancient, oriental, and medieval art; including the
Renaissance and the seventeenth and eigtheenth centuries. Though he himself was
a distinguished painter and illustrator, Albert-Charles-August Racinet
(1825–1893) is best remembered for two monumental color-plate publications he
edited: Le Costume historique (Historic Costume) and L'Ornement
polychrome (Color Ornament).
Raeburn, Michael. 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. Of its type, a good account of
the general
Ranucci, Ernest R. 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. Gift of Lorenzo Logi. Of note is that it contains example of Angiolo Logi’s cluster puzzle work.
Rawson, Phillip. First came across the term ‘simulacrum’ page 150 from this book. Islamic pattern p. 90. Ray, Simon. Indian & Islamic Works of Art. Self Published, 2017, pp. 177-178 (2019) Rayner, D. 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. Juvenile.
Read, Ronald C.
Reader’s Digest Books and Articles – see Moore, Alison, Keeton, Greg.
Rees, Martin. Has Escher’s * and * pp**.
Reichelt, Gotz-Peter. On his interlocking wood carved animal puzzles, namely cluster puzzles. Most pleasing indeed, with quality examples throughout.
Renko, Hal; Edwards, Sam. ‘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. Although on astronomy, has sideways references to mathematics, namely with polyhedra, pp. 48-51, Jamnitzer and Kepler p. 57.
Reyes, Encarnación and Inmaculada Fernández. 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. Small format hardback, 15 Chapters, 272 pp. Some popular philosophical musings as to the attraction (or ‘spell’) of mathematics. Of limited interest. Too advanced in parts, but still largely accessible. No tessellation or Escher. Perhaps of most interest is on the cycloid, pp. 160-161. Also occasional geometry throughout the book.
Richardson, Margaret H. By a pioneer of cluster puzzles. ‘A biographical sketch’, as quoted by Anne Williams.
Riley, Noel. Examined on the likely possibility of tessellation, but not so, at least of any substance.
Robertson, Bruce. 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
Rogers, James T.
Rogers, Nigel. Consultant editor Dr Ian Gordan. Rooney, Anne. The Story of Mathematics. From creating the pyramids to exploring infinity. Arcturus Publishing Limited, 2008. (30 November 2019)
Roojen, Pepin van 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. Rangoli and Islamic tilings p.
21. Use of Escher’s
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. All books are text only.
Roza, Greg. Gift of Jeffrey Price. Has
Escher cover of
Rubin, Don.
Rucker, Rudy. A popular account of advanced concepts. A minor study worked on on 2 January 1990, first seen at Grimsby central library, long since deleted from stock. Nothing on tessellation per se in my study. The book is available for free
on his website (and with other publications of his, notably
Russell, Betrand. 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. One book of the seven-part
‘Mathematics for the Majority’, series, of which I have two. The book seems to
have been compiled by a ‘project team’, with one primary author stated. The
books are stated as ‘Chatto & Windus for the Schools Council’, which thus
gives the intended audience. The back cover states ‘This Schools Council
project was set up to further the teaching of mathematics in secondary schools
to children of average and less-than-average ability’. Also see Of ‘pattern’ in the broader sense, of number and geometry. The topics of this book are broadly out of my mainstream interest, but it still has isolated aspects of interest. There is no tessellation. Symmetry pp. 25-28, Polyhedra pp. 36-37, Golden Section pp. 61-63. Has interesting book list, pp. 66, with unknown E J. James reference and series of ‘Topics of Mathematics’, Cambridge.
Sabin, Francene and Louis. ‘ From a reference in Williams,
although found first by ‘favoured chance’ on the web, of the first chapter,
Sackett, Dudley.
Sackson, Sid. Gardneresque. Stated on the back cover as ‘diversified collection of 38 remarkable, intellectually stimulating indoor games…. many of the book’s best games are the invention of the author’. Martin Gardner praises it. In six sections. Each section begings with a small essay, followed by the games. Has a useful section on ‘short reviews of ganes in print’, pp. 188-221. Sackson is widely recognised as an authority on games, and game history. Of general interest, but much of the material, being non-geometrical, is of little direct interest. It is ideal for reference purposes, but not for actual study. Sagan, Carl. The Cosmic Connection. Book Club Edition. First published in 1973. Second edition 2000. Seen on Internet Archive as ‘community texts’ (24 December 2019). Makes occasional use of Escher prints, albeit without any commentary at all. Another World, Part 1 Wikipedia: … an expanded edition with contributions from Freeman Dyson, David Morrison, and Ann Druyan was published in 2000 under the title Carl Sagan's Cosmic Connection. The book contains artwork by Jon Lomberg and other artists. Of note is that Sagan had a decided interest in Escher. Also see his Dragons of Eden: Speculations on the Evolution of Human Intelligence for more of Escher’s works. Further, he used Another World as a background to the film of the (famed) series Cosmos (Episode 10: The edge of forever). (As noted in a Facebook Escher group posting by Jose David Avila Arevalo). Note that this was not mentioned in the book of the series. It would be interesting to know more of Sagan’s interest. ————. Dragons of Eden: Speculations on the Evolution of Human Intelligence. Random House. First published 1977 (and numerous reprintings). Seen on Internet Archive (24 December 2019). Makes occasional use of Escher prints, albeit without any commentary at all. Plane Filling II on cover, but not on 1977 edition! Reptiles print inside cover. Three Spheres, desaturated, is used on all nine chapter headings. Plane Filling II, p. 78. Stars, p. 231. Escher is not mentioned in the index or seemingly credited elsewhere aside from the captions Wikipedia: ... the author combines the fields of anthropology, evolutionary biology, psychology, and computer science to give a perspective on how human intelligence may have evolved. … The book is an expansion of the Jacob Bronowski Memorial Lecture in Natural Philosophy which Sagan gave at the University of Toronto. Salvadori, Mario. Occasional crossover to mathematics.
Sanchez, Miguel. No Cairo pentagon.
Sarcone, Gianni A. and Marie-Jo Waeber. Although not a maths book it
is included here as it has crossovers. Popular account. Yoshifugi Utagawa (not
credited) cover and p. 27, with elephants and children; Duck/Rabbit p. 58 in
Fliegende Blatter, 1892, Escher’s
Sardar, Ziauddin, and Iwona Abrams. Ed. Richard Appignanesi.
Popular account of chaos, as a part of a series of like books.
Sarhangi, Reza (Ed).
Sarhangi, Reza (Ed).
Sarhangi, Reza (Ed).
Sarhangi, Reza (Ed).
Sarhangi, Reza (Ed).
Sarhangi, Reza; Carlo Séquin (Ed).
Sarhangi, Reza; Moody, Robert V. (Ed).
Sarhangi, Reza; John Sharp (Eds).
Sarhangi, Reza (Ed). 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 Quote: 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. Free, college library. A serious, though still readable discourse. I find the book a little odd. It is essentially a study of a study! I can’t see how I could gain from re-reading this.
Sattin, Anthony and Sylvie Franquet. 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. Many occasional references to Escher, mostly in passing. Those of note include pp. 24-26, 76-79.
————. 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. Small format paperback, albeit
of 214 pages. Of limited interest, due to the nature of Sawyer’s writings,
which largely focus on calculation, not my forte. although there are chapters
ostensibly of interest, such as Chapter 6, ‘Geometries other than Euclid’s’,
and Chapter 12, ‘On Transformations’, these are still advanced for me. As such, I find Sawyer’s writings (like Coxeter’s), not
conducive to my understanding (my fault, not theirs!). From Wikipedia: Walter Warwick Sawyer was born in St. Ives, Hunts, England on April 5, 1911. He attended Highgate School in London. He was an undergraduate at St. John's College, Cambridge, obtaining a BA in 1933 and specializing in quantum theory and relativity. He was an assistant lecturer in mathematics from 1933 to 1937 at University College, Dundee and from 1937 to 1944 at University of Manchester. From 1945 to 1947, he was the head of mathematics at Leicester College of Technology. In 1948 Sawyer became the first head of the mathematics department of what is now the University of Ghana. From 1951 to 1956, he was at Canterbury College (now the University of Canterbury in New Zealand). He left Canterbury College to become an associate professor at the University of Illinois, where he worked from winter 1957 through June 1958. While there, he criticized the New Math movement, which included the people who had hired him. From 1958 to 1965, he was a professor of mathematics at Wesleyan University, where he edited Mathematics Student Journal. In the fall of 1965 he became a professor at the University of Toronto, appointed to both the College of Education and the Department of Mathematics. He retired in 1976. Sawyer was the author of some 11 books. He is probably best known for his semi-popular works Mathematician's Delight and Prelude to Mathematics. Both of these have been translated into many languages. Mathematician's Delight was still in print 65 years after it was written. Some mathematicians have credited these books with helping to inspire their choice of a career. Sawyer died on February 15, 2008, at the age of 96. He is survived by a daughter.
————. Small format paperback, albeit
of 346 pages.Of limited interest, due to the nature of Sawyer’s writings, which
largely focus on calculation, not my forte. The first in the series of four books (of which I have two) on the
pemise of ‘Introducing Mathematics’. Better than his other book
————. Written in the same vein as with the first book in the series, as detailed above, and of which the same comments apply. Not recreational maths.
Sawyer, W. W (ed.) Very much of its day, with much calculation, although that said, much is readable.
Scharf, Aaron and Stephen Bayley. Escher’s
Schattschneider, Doris. Revised edition 2004 (23 March 2010) Indispensable! Highligh after highlight.
Schattschneider, Doris and Wallace Walker. Cairo like tiling, p. 26, and
a short discussion as to Escher’s. I also have a German edition,
Schattschneider, D. and M. Emmer (editors). 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.
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
Problems pp. 112-126 (129-138), but without tilings. Volume III appears of a more technical nature, mostly text,
of few diagrams. Nothing on tilings and polyhedra.————. 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. 1963, Small format, 83 pages. Stated as for teachers to enliven lessons. Covers a broad mathematical puzzle spectrum: Oddments in Artithmetic, Oddments in Algebra, Oddments in Geometry, Miscellaneous Oddments, Answers, Book List (although the book list is not seen!). By far the most interesting is on Oddments in Geometry, although there does not appear to be anything too original here. Discusses Geometric Dissections, pp. 52-54, including Perigal’s dissection pp. 52-53. Although most is popular, it has all been seen before. No tessellation. The author, largely unknown, appears to be of a puzzler/mathematician, as he has (at least) two other like books to his name.
————. Small format hardbook, 96 pages. Dudeneyesque. Covers a broad puzzle spectrum: Mathematical Puzzles, Logic Puzzles, Crossword Puzzles, Word Puzzles, Vocabulary, Literature and General Knowledge, Oddity-Box, with solutions. Nothing geometrical. To what, if any extent these are original is not made clear.
Sealey, L.G. W. Juvenile 10-years-old audience.
Seckel, Al. 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.
Seitz, William C. 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. https://www.moma.org/calendar/exhibitions/2914?locale=en
Serra, Michael. 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.
Seton-Williams, Veronica and Peter Stocks. Obtained, by a chance finding, of possible Cairo tiling interest. Described as a description and travel guide, and furthermore of an scholarly (although still readable), extensive nature, of a narrow fomat paperback, of 743 pages! Simply stated, this was seen at a car boot sale, and of which it was thus impractical to view for Cairo tiling aspects. On the off chance of usefuness, duly obtained. Upon a more leisurely read, there was no Cairo tile references in any capapacity. But there might have been! The matter is at least settled, rather than regretting having left the possibility open-ended. Previously, the term Blue Guide (from the colour of the cover) was unknown to me. From Wikipedia:
Seymour, D; Britton, J. Cairo tiling, but not attributed, p. 39.
Seymour, Dale. Advanced Juvenile.
————. 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.) Card and board games.
Shaw, Sheilah. 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. Of jigsaw puzzle interest. 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.
————. Of jigsaw puzzle interest. 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
————. Of jigsaw puzzle interest. Shubnikov A. V. and N. V Belov. 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 all aspects. Somewhat difficult to assess. Largely of an academic nature, but with occasional aspects of a recreational level. Cairo tiling p. 180, albeit by default of quadrilateral tilings p. 176-179. Escher lizards, unicorns figures pp. 228-229 (colour plate), birds p. 364, winged lions p. 365. Interestingly, as regards to the winged lions’, Schattschneider [1990] also refers to this as a ‘winged lion’, despite these creatures bearing little resemblance to a lion, wings or not. Was her description taken/influenced by Shubnikov? She knew of this book.
Sibbald, Tim M. and Miranda
Wheatstone.. ‘Advancing Escher art through generalization’. The Escher aspect is somewhat overstated.
Singh, Simon.
————. General interest. The Simpsons and Their Mathematical Secrets. Bloomsbury, 2013 (28 December 2019). Escher 91-92, in relation to Relativity.
Singmaster, David. Small format paperback 68 pp, of condensed text. One of the earliest books on the Rubik cube, at the height of the craze. Written from a group theory viewpoint, with much of the text way beyond my understanding. Likely, I quickly gave up on this! Mentions a few high profile names who I didn’t know were interested in this, such as Roger Penrose and PeterMcMullen.
Silverman, David L. 100 various puzzles and games under various descriptions, all at a popular level, such as ‘Potpurri I’, ‘Bridge’, ‘Chess and Variations’, ‘Checkers and Variations’ etc., with each puzzle on a single page followed by the answer. No tiling or polyhedra.
Sirett, Natalie. P. 18. Cube
illusion of ‘three ways’ The book
lacks a bibliography.
Slade, Richard. The jacket describes as ‘This
is a fascinating book for children….’, which gives the intended audience. Slade
describes himself as a teacher of handicrafts. He is also the author of nine
other books on handicrafts, with possible interest Has an interesting historical French curve source reference, page 16, crediting this to a ‘Professor French, a mathematician’ different from others. Islamic design on front cover, and repeated p. 37. Eight chapters, with Chapter 6, the most indepth, and of most interest.
Slocum, Jerry, and Jack Botermans. 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.
————. 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.
Smeltzer,
Victoria and Patricia Smeltzer. Juvenile, 10-year-old.Tessellation p. 75. Hexagons, not worth mentioning.
Smith, Cyril Stanley. Has Cairo tiling diagram, without attribution, found indirectly in a excerpt page in the Indian journal ‘Resonance’, of June 2006.
Smith, Thyra. Juvenile.
————. Juvenile.
Smith, Charles N. 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. 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
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 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. 271 popular logic puzzles in four parts. Of minor recreational interest, nothing more. Has occasional stories on mathematicians. Overall, I have limited patience with the genre. Snowden, Robert, Peter Thompson and Tom Troscianko. Basic Vision. An introduction to visual perception. Oxford University Press. First published 2006 (22 June 2019) Of vision interest. Of a broad popular account, with leanings at times to the academic. Escher print ‘Ascending and Descending’ p. 198, albeit only discussed in passing. P. 96. Cafe wall illusion. I was under the impression that this came about by the cafe wall tiling in Bristol, but the book contradicts this, saying it was known well before. Investigate. P. 123. Idea for Ponzo illusion, p. 123, fade upper bar as in perspective gradient, and see the effect. 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. 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: A later colour edition was subsequently seen in both Cleethorpes and Grimsby libraries.
Staněk, V. J. Not really a maths book, has occasional pattern by default.
Stannard, Dorothy (Editor). 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. Camera obscura conjectures.
Steinhaus, H. Many aspects of recreational interest. Chapter 4, tessellations pp. 75-83.
Stephens, Pam. Juvenile content, despite the serious title, of only 40 pages. Stephens apparently wrote the entire text, with the artwork (tessellations) by Jim McNeil. Pages 1 and 2 cut out, hence this lacks bibliographical detail.
Stevens, Peter S. Handbook of Regular Patterns. An Introduction to Symmetry in Two Dimensions. The MIT Press, Cambridge, Massachusetts and London, England). First printed 1981, Third printing, 1987 (c. 15 December 2007, through receipt). First saw 4 October 1990 First saw 4 October 1990 (ordered through the library), this sparking a concerted study of the day, throughout the month of October. Illustrated throughout with various Escher periodic drawings. Occasional Cairo tilings arising from my studies, although not directly from the book itself. A most pleasant read, with a crystallographic leaning, best described as a compilation (as the author, an architect, admits) of tiling and patterns throughout the ages. A feature, scattered liberally throughout the book, is of geometric Escher-like tessellations, of which I believe acted as the moving spring of my own. These would appear to be by Stevens, albeit there are doubts here, as this is not made explicit. In the preface Mollie Moran is credited with drawing most of the illustrations, hence my uncertainty. If there's one criticism, the illustrations need more detail; sometimes nothing at all is given, whereas with others there is only a bare minimum. Of direct interest: Houndstooth tiling (not standard model), pp.195-196. Said to be from Sandwich Islands, of which likely this refers to Owen Jones’ Grammar (who is mentioned in the bibliography). Dogbone tiling, p. 294, Arabian. ————. 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.
Stephenson, C. and F. Suddards. A Text Book Dealing With Ornamental Design For Woven Fabrics. First edition 1897, Methuen & Co. Ltd and Fourth Edition. Methuen & Co. Ltd 1924. N.B. Not seen the first edition but I have the fourth edition as a PDF. (March 2019) Of houndstooth and weave interest. Very much in the Lewis Day tradition, from a weave perspective. Of most note is p. 16, of Plate III, Fig. 9, of a houndstooth (but not stated as such) in black and white as a counterchange design, and further not as a weave but of the tessellation type. I presume that this is also in the first edition. Stewart, Ian. Of limited interest, with somewhat technical, advanced concepts way beyond me. 339 pp. paperback. Topology, Chapter 10 pp. 144-158. No tessellation, Escher. No plans (2018) to re-read.
————. From a reference on an old cardboard ring binder, of 3 May – 21 days library book. The content is now (2018) long forgotten. I do not recall any studies arising from this.
. ————. Popular account, but of general interest only, no tessellation.
————. Of limited interest.
————. 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
————. Popular maths.
————. Largely popular account of hard to understand concepts. Quasicrystal tiling p. 101-103. Chapter 12, Squaring the Unsquarable, Geometric Dissections pp. 168-171. No references to Escher, tessellation or tiling. Shortage of time (2018) forbids a re-read.
Stewart, Ian and Martin Golubitsky. Occasional Escher pictures, Circle Limit IV, p.45, Lizards 237; Penrose tiling p. 95, Kepler’s Aa to Z patch, p. 96; Pólya diagram p. 239, with Pólya’s annotations, but generally all these references are in passing only.
Stewart, Desmond. Part of a 20-book Time-Life series. Not on tilings as such, but of course with many side references. Only tiling aspects of interest pp. 150-151 and 156-157, with double page spreads.
————. and the editors of the newsweek book division. Recorded on a menu card, c. September 1987. A single study of 11 July 1988 study. General discussion on the Alhambra without a dedicated study of tilings per se. Many pictures have not been seen before. Although tilings do appear, this merely illustrates the discussion. Of most interest pp. 15, 33, 73, 101, 125, 183, where a tiling is shown full on, as a square each time. Sturgis, Alexander. Magic in Art. Belitha Press Limited, first published 1994 (18 August 2019) Juvenile, 32 pp. The cover caption states: Perspective, Tricks and Illusions. A series of topics are discussed over a two-page spread, with most of the interest being ‘The Impossible World of Escher’, 16-17, illustrated with Belvedere, Relativity and Ascending and Descending, with brief commentary. Relativity is also on the front cover. Of standard fare. Somewhat to my astonishment, given a juvenile book, I found not one but two aspects new to me! This concerned excised columns appearing in Leonardo's Mona Lisa and op art by Victor Vasarely’s son, Jean-Pierre Yvaral, also known as Jean-Pierre Vasarely, whose work I was unfamiliar with! Sutton, O. G. Semi-popular, although tending towards the advanced.
Sykes, Mabel. 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. Overweight coffee table book,
occasional maths. Escher’s print
Tammadge, Alan and Phyllis Starr.
Tapson, Frank. Chance finding. Intended for a 11-16 audience, albeit even here, much of this remains obscure. Gives simple definitions of mathematical terms. Of perhaps most note is a Cairo tiling (not attributed) on p. 139.
Taylor, Don and Leanne Rylands. Small format paperback, 50 pp. In short, a how-to on Rubik’s Cube, published with many others at the height (1981) of the craze. Quite where the ‘92 classic games’ is derived is unclear; it’s simply a monologue on Rubik’s Cube. This is perhaps better than most of the day, at least in theory, with colour diagrams, which is surely better than line diagrams with initial letters from colours. Taylor and Rylands are both (mathematical) Australians, hence the Australian publication. Such books are essentially in my past now (2018). There is simply a lack of time to re-study.
Taylor, Don. Very small book. The Chronicler (Lord High Keeper). Fred Learns the New Mathematics. Continua Productions Ltd 1978, 160 pp (‘First saw’ c. 8 December 1989 (day of study). Book is not to hand, lost in storage. I only have a photocopy of relevant pages, and so the discussion below is as best in the circumstances permit, pending a more detailed piece upon finding. This seems to be a children’s book, of which the author’s name is unclear. Of most interest is Chapter 4, ‘Tessellations and Topology’ with tessellations of pp. 146-148. This includes both simple, pure tilings as well as Escher-like, mostly tilted somewhat extravagantly, with bird, ‘flat chested thrusters’ (dinosaur-like), ‘curved back leaper’, ‘phantasmagorial fibbertigibbet’ (dog-like). Phantasmagorial - having a fantastic or deceptive appearance, as something in a dream or created by the imagination. having the appearance of an optical illusion, especially one produced by a magic lantern. Changing or shifting, as a scene made up of many elements. Flibbertigibbet - is a Middle English word referring to a flighty or whimsical person, usually a young woman. In modern use, it is used as a slang term, especially in Yorkshire, for a gossipy or overly talkative person. One of the pure tilings, reminiscent of a fish, led to extensive studies.
Thé, Erik, Designer. 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,
As given by Andrew Crompton. Author unknown. Thomas, Briony G. and Michael A. Hann. Patterns in the Plane and Beyond: Symmetry in Two and Three Dimensions. 2007. The University of Leeds and the authors. Ars Textrina, No. 37 Cairo tiling pp. 52-53, 70-71, 79. Stated (incorrectly) as equilateral. Thomas, Frank and Ollie Johnston. 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 Wentworth. A single-sheet study of this
is dated 31 March 1988, of which by the page numbers quoted is clearly of an
edition by Thompson (1,116 pp.), rather than the abridged (346 pp.) by Bonner.
Likely this was by following a reference somewhere (possibly
From Wikipedia: On Growth and Form is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942. The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts (phyllotaxis); and Thompson's own method of transformations, showing the changes in shape of animal skulls and other structures on a Cartesian grid. The work is widely admired by biologists, anthropologists and architects among others, but less often read than cited. Peter Medawar explains this as being because it clearly pioneered the use of mathematics in biology, and helped to defeat mystical ideas of vitalism; but that the book is weakened by Thompson's failure to understand the role of evolution and evolutionary history in shaping living structures. Philip Ball and Michael Ruse, on the other hand, suspect that while Thompson argued for physical mechanisms, his rejection of natural selection bordered on vitalism….
Thorndike, Joseph J. (Editor-in-Chief). ‘Escher's Eerie
Games’. 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?
Thornburg, David D. 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
Thyer, Dennis and John Maggs. 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. 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. A scholarly account in a popular manner (in contrast to mostly others, of a lightweight nature). No maths at all.
Tóth, Fejes L. 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. 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.
Travers, James.
————.
Tufnell, Richard. Some minor tessellation studies, nothing in the way of originality.
Turner, Harry. 72 pp. Drawn to my attention by Alan Bridges of art college. First saw 22 February 1993, where I seemingly borrowed and photocopied the entire book the next day, upon which I then studied on the sheets themselves. I canot recall if I have subsequently obtained the book. I cannot find it if so; I get mixed up with other similar Dover publications by Locke and Willson.
Tyler, Tom. 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 http://www.hamleys.com/explore-life-history.irs, albeit this is most lightweight indeed.
Varnedoe, Kirk. From a reference in
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 Puchinger.
Valette, G.
Van Delft, Pieter, and
Jack Botermans.
Vecht, N. J. van de.
Veldhuysen, W. F. (the author is unclear; Veldhuysen wrote
the foreword, hence placed accordingly). On a Escher theme of ex
libris, on a competition marking the 100
Vermeulen, Jan W. Escher's writings collected.
Vorderman, Carol. Tessellation 130-131, Polyhedron 152.
————. Covers the basics, but even here, I’m struggling in more places than I care to (embarrassingly) list…
Wade, David.
————. Geometric Patterns & Borders. Wildwood House Ltd. 1982 (16 September 1995) The premise is of a geometric pattern book, with line drawings and colouring (in black and white) from various countries around the world. Text is seemingly purposefully kept to a minimum at the beginning of the book. The book is (regrettably) not paginated, but rather is ordered by diagram numbers. No bibliography. Has many interesting designs, worthy of study, of which I return to at intermittent intervals. Countries of origin generally accompany the diagrams, but no other detail, which is frustrating where more specific detail is sought. Nonetheless, even with shortcoming of presentations, the book is a veritable visual feast, to be returned to time and again. No Cairo tiling as such. Diagrams of interest include: 193, double axe head tiling 194, Cairo tile-related bowtie tiling. 260, houndstooth, stated from Hawaii, likely referring to the Owen Jones reference in Grammar of Ornament, p. 15. However, Wade’s instance is different in proportion, based on an isometric grid. 333, Cairo tile and regular hexagon in combination. 383, houndstooth in nature, of a ‘pixelated weave’ type, and is briefly discussed in the introductory text, ‘… from African basketwork…’. However, beyond this, no specific detail as to source. 555, houndstooth as a frieze.
————. 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. Complimentary copy from Springer. Popular account. Lots of interest. Chapter specifically on tiling, with frequent references to Escher.
Wallis, Denis (Principal writer). One minor reference to Escher, p. 87, with Waterfall and general text.
Walker, Michelle. 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.
Juvenile, of no interest.
Walter, Marion.
For children 8-11. Tessellations pp. 57-59. Has a most intesting biblography, with some tesellation references not seen before!
Wark, Edna. 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. 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 Watson, William. Colour in Textile Designing. Elementary Weaves and Figured Fabrics. First edition 1912. Second edition 1921 (Internet Book Archive and cs.arizona.edu). Longmans, Green and Co. There is an at least a 7th edition. 369 pp. (2019) PDF Of fabric interest. Referenced in Grünbaum and Shepherd’s 1980 Satins and Twills article. Some confusion as to specifics here. Watson has other books to his name. The book is replete of interest. Liberally illustrated, with nearly every page containing diagrams. A must have! Obvious houndstooth (but not named as such) p. 156, 164. Shepherd’s Check p. 157 Watson, William (ed.) The Great Japan Exhibition: Art of the Edo Period 1600-1868. Royal Academy of Arts London 1981-2. Catalogue published in association with Weidenfeld and Nicolson, London (22 June 2019) Has minor aspects of pattern and tiling.
Weaire, Denis. Of note is that in the preface, by Charles Frank, in so many words surely is discussing the Cairo tiling, seen at Glasgow Physics lab!
Wells, A. F. Wildly quoted in tiling mathematics despite being a chemistry book! Cairo tilings pp. 24-25, in the context of Laves tilings, although not named as such (8 February 2016). This is pleasing as Wells mentions, p. 24, the aesthetics, with ‘… a very elegant arrangement of pentagons…’.
Wells, David. 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.
————. Cairo line drawing, and discussion p. 23.
————. 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.
————. Popular account of properties of numbers, of the same premise of Neil Sloane, but much more accessible.
————. 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. Foreword by Coxeter. Popular account, of 119 polyhedra. Discusses colouration (although the book is in black and white) and history.
————.
Werneck, Tom. Small format paperback, 112 pp, with instructions for solving the Pyraminx, a Rubik’s cube-type puzzle, published at the height of the Rubik cube craze. The puzzle is more properly known as the Pyraminx. Originanally, I thought this was Rubik-inspired of the day until latterly re-reading the book and seeing the Wikipeda entry: Fom Wikipedia: On Tom Werneck, of whom I was
unfamiliar (Form Boardgamegeek):
Wesley, R. (ed.) Very much of its day, with much laborious calculation.
Weyl, Hermann. Although this little book is much praised in the tiling world, I must admit that for my purposes I was a little disappointed with it. Certainly, it is of interest, but the audience it is intended for is not clear; there are both recreational and academic instances of study. Tiling as such is at a minimum, subsumed under ‘Ornamental Symmetry’. Of note is that an earlier edition, in Russian, of 1953? shows Escher’s Lizards, the first such usage his work as cover art.
Wheeler, Francis Rolt- (Managing Editor). Small format hardback. Semi-popular,semi-scholarly account of mathematics. Of most interest is geometry, Chapter 5, pp 107-154, with Kepler pp. 112-113, Perigal dissection of Pythagoras diagram. p. 114, Designs on Tombs of Bernoulli, Archimedes, p. 137. Liberally illustrated, but a bit too advanced for me. No tessellation,per se, although there is ‘tessellated muliplication’, p. 44, of which I was unfamilar with. Looking on Google, I cannot find any other instances of this description. From WorldCat: I. Astronomy, by W. Kaempffert; introduction by E.E. Barnard.--II. Geology, by H.E. Slade and W.E. Ferguson.--III. Physics, by G. Matthew. Electricity, by W.J. Moore.--IV. Chemistry, by W.A. Hamor; introduction by C. Baskerville.--V. Biology, by Caroline E. Stackpole.--VI. Zoology, by W.D. Matthew. Botany, by M.E. Latham; introduction by W.T. Hornaday.--VII. Anthropology, by F. Rolt-Wheeler. Medicine, by T.H. Allen; introduction by F. Starr.--VIII. Pure mathematics, by L.L. Locke. Foundations of mathematics, by C.J. Keyser. Mathematical applications, by F. Bellinger; introduction by C.J. Keyser.--IX. Art, by B.S. Woolf. Literature, by F. Rolt-Wheeler; introduction by E.J. Wheeler.--X. Schools of Philosophy, by C.G. Shaw. Sociology and political economy, by L.D. Abbott. Ethics, by F. Rolt-Wheeler; introduction by H. Münsterberg.
Whistler, Rex and Laurence Whistler. 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. Juvenile, mostly patterns in the real world. Occasional tessellation.
————. Recommended by art class tutor Peter Bendelow, c. 1983.
White, William F. Lots of recreational aspects, with most of interest to me: geometric dissection pp. 91-99, tiling p.100, four-colour theorem p. 120-121.
Whitelaw, Ian. 160 pp, small format hardback. Popular account, of 11 chapters, in bite size.
Whitehouse, F. R. B. Of game interest. In-depth
treatment, although of a popular nature. Liberally illustrated. Twelve chapters, of particular interest
Chapter X, ‘Jig-Saw Puzzles’, pp 84-85, on John Wallis, albeit lightweight in
depth. Book quoted in Hannas,
Williams, Anne D. 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.
————. 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
Williams, Robert. Of most note is a Cairo tiling pp. 38, 204, in the context of the dual and transfromation between squares and basketweave tessellations. Quite how best to describe Williiams is unclear. Architect, designer? He deos not appear to be a mathemtaican per se. Further how much of the book is original with him is unclear. I suspect, from the books and articles quoted, that he is borrowing heavily. Of note is that on p. 42 he quotes the most obscure D. G. Wood Cairo tile reference. Of most interest per se is Chaper 2, ‘Natural Structure and the Two Dimensional Plane’, on tilings and circle packings, pp. 31-52.
Willson, John. Slim volume, of just 30 pages. Cairo tiling plate 3. (Neglected, or not noticed, until 7 May 2013!) Very pleasing indeed, with many simple, but interesting tilings, and ideas thereof. Discussion of tesellations, in a simple manner, pp. 1-14, 15-18, these being separated by wirfeame plates. Studied tessellating letters p. 15?
Wilson, Eva. 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. (6 July 2017) Popular account.
————. Wiltshire, Alan. 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.
————. 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
————.
Wood, Elizabeth Armstrong. 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. LOOK FOR. From a reference in Wood, Donald G. Space Enclosure Systems. Identification and Documentation of Cell Geometries. Bulletin 203. Engineering Experiment Station, The Ohio State University, Columbus Ohio. 1967 or 1968, 52 pp. No publication date is given in the booklet (11 December 2012). An obscure publication, seemingly little known or quoted in tiling circles, when perhaps it should otherwise be. Although of a polyhedral nature, in the form of prisms, has occasional tiling aspects of note. Much of his work here, and elsewhere in the book, is in regards to modelling prisms, in cardboard. This bulletin came to my attention (belatedly) from a footnote in The Geometrical Foundation of Natural Structures by Robert Williams, p. 43, as regards my Cairo tiling interest. Has occasional Cairo-tile instances (non-attributed), of an equilateral pentagon of pp. 3-5, 30-31, derived (and credited) from MacMahon and Cundy and Rollett’s works. Wood makes a curious observation as regards tilings with equal length sides, with the Cairo tiling being one of five such instances (with the others being an equilateral triangle, square, hexagon, and rhomb); as such, I do not recall seeing this simple and possibly significant (in relative terms) observation elsewhere. Donald G. Wood (1922-2011), was a professor of industrial design in the School of Art at Ohio State University, Columbus, Ohio, US. Wood gives 15 references, some popular, and known, and some obscure, never before (as far as I know) quoted in tiling circles. In the hope of finding pentagon tilings, or indeed interesting tilings in general, I found (historical) references on Lewis, Davey, and Egleston, but no tiling as such was found in their respective works. Note also that there is one other (later) like publication by Wood, Space Enclosure Systems: The Variables of Packing Cell Design, Bulletin 205, 1968, 52p. Not seen.
Wood, Mary. 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
Woodman, Anne; Eric Albany. Many pages concerning Escher-like tessellations, beginner’s level, very poor standard indeed, even for children.
Yarwood, A. 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. 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. Mostly board games.
Zusne, Leonard. 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
Aside from the en masse listing above, it is also possible to compile inventories of specific aspects, such as spiral tiling. In short, this is a convenience, to save wading through the above extensive listing.
A compilation of 1 April 2020+, primarily for purposes of aiding Peichang Ouyang et al (including myself) paper ‘Generation of Advanced Escher-like Spiral Tessellations’. Books and Articles Burgiel, H. and M. Salomone. ‘Logarithmic spirals and projective geometry in M.C. Escher’s Path of Life III’. Journal of Humanistic Mathematics, Volume 2 Number 1, January 2012, pp. 22-35. Some advanced mathematics of a substantial article. Oddly, Escher’s Path of Life III is not shown, which seems strange given the premise, and the frequent mentions throughout. Gailunas, Paul. ‘Spiral Tilings’. In Bridges 2000, 133-140 Nice treatment indeed. Comments on Grunbaum and Shephard comment on little literature on the subject. Building on their work, Gailunas shows a ‘Zig-zag spiral tiling’. It is not entirely clear the extent of originality here. I suspect it may be based on others, with prominent use made of the versatile. Profusely illustrated. No Escher-like tilings. Gardner, Martin. ‘Extraordinary nonperiodic tiling that enriches the theory of tiles’. Scientific American. January 1977 110-121. On Penrose tiling. Minor mention and illustration of Voderberg spiral, p. 111. Reprinted in Penrose Tiles to Trapdoor Ciphers, pp. 2-4. Goldberg, M. ‘Central Tessellations’, Scripta Math. 21, 1955, 253-260. NOT SEEN Grunbaum B. and Shephard, G. C. ‘Spiral Tilings and Versatiles’, Mathematics Teaching, no.88, Sept. 1979, pp. 50‑51. NOT SEEN Grunbaum, Branko and G. C. Shepherd. ‘Some Problems on Plane Tilings’, in The Mathematical Gardner by David A. Klarner. Pringle, Weber & Schmidt Boston, 1981 pp. 167-196 Amid a discussion on various problems on plane tiling, a spiral discussion, with ‘Problems 10-12’, pp. 191-194. Of particular note is that Problem 12 asks: ‘Give a precise definition of a spiral tiling’, in relation to saying what exactly a spiral tiling is. Is this the first explicit instance? Voderburg tile as a plane tiling and spiral tiling pp. 189-192, 196, Versatile 192-194 as a spiral tiling. Grunbaum, B. and Shephard, G. C. Tilings and Patterns. W. H. Freeman, 1987. 512-518 related p. 123 Chapter 9.5 on spiral tilings, pp. 512-516, 518. Begins with mention of Voderburg. Note and references pp. 517-518, where they lament the lack of literature, but not here the definition [CHECK] Grunbaum, B. ‘Patch determined tilings’. The Mathematical Gazette. 31-38. In the context of ‘patch determined tilings’, a five-arm spiral tiling is shown, Fig. 10. No Escher-like tilings. Hatch G. ‘Tessellations with Equilateral Reflex Polygons’, Mathematics Teaching, no.84, September 1978, p.32. NOT SEEN Kanon, Joseph. ‘The Saturday Review December’ 16 1972 ** Sphere Spirals Klaassen, Bernhard. ‘How to Define a Spiral Tiling?’ Mathematics Magazine December 2017, pp. 26-38 On the difficulties of defining a spiral tiling, implicit building on Grunbaum and Shephard’s conjecture. Shows Voderburg spiral. Largely popular, with occasional advanced maths. Lalvani H. US Patent 4,620,998, 1986. Cited in Meta Architecture, in Architecture and Science (ed. Di Cristina G.), Wiley Academy, 2001. Occasional spiral-like tilings, but not stated as such. Mann, Casey. ‘A Tile with Surround Number 2’. The American Mathematical Monthly. Vol. 109 No. 4 April 2002 pp. 383-388 On coronas, something of which I am not particularly interested in. In the course of the ‘surround’ study, there is a Voderberg tile discussion, but not in the context of spirals. Marcotte, James and Matthew Salomone. ‘Loxodromic Spirals in M. C. Escher's Sphere Surface’. Journal of Humanistic Mathematics Volume 4 Issue 2 July 2014 Palmer, Chris K. ‘Spiral Tilings with C-curves Using Combinatorics to Augment Tradition’. In Bridges Renaissance Banff 2005, pp. 37-46 The use of the word spiral in the title is somewhat overblown; it is then not mentioned again until the references page! Of no real interest as to spirals as such. Pickover, Clifford. ‘Mathematics and Beauty: A Sampling of Spirals and Strange Spirals in Science, Nature and Art’. Leonardo Vol. 21, 1988, No. 2, pp.173-181 A good general, popular guide as to all things spiral applications as to the real world, and more, with much interest. No tiling or Escher-like as such.
NOT SEEN Sharp, J. ‘Golden Section Spirals’. Mathematics in School. November 1997pp. 8-12 Of general interest in spirals. No tiling. Notable authors such as Keith Devlin and Ian Stewart are taken to task for misattributing the Nautilus shell cross section as a Golden Section Spiral. Simonds, D. R. ‘Central Tesselations (sic) with an Equilateral Pentagon’. Mathematics Teaching No. 81, December (1977), pp. 36-37 ————. Untitled note Mathematics Teaching 84 (1978), p. 33 Stock, Daniel L. and Brian A. Wichmann. ‘Odd Spiral Tilings’ Mathematics Magazine Vol. 73, No. 5 (Dec., 2000), pp. 339-346 Seemingly borrowing from Grunbaum and Shephard, Stock and Wichmann comment on the little literature on the subject. Building on their work, with a regular decagon on odd numbers of arm spirals, they show any number of odd numbered spiral tilings. A versatile is also shown. No Escher-like tilings. Tóth, Fejes L. Regular Figures. Pergamon Press 1964 (12 December 2010), partial copy, of Chapter 1 up to p. 43... Regulare Figuren. Akademi kiado, Budapest , 1965. English translation 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). Voderburg, H. ‘Zur Zerlegung der Umgebung eines ebenen Bereiches in kongruente’. Jahresbericht der Deutschen Mathematiker-Vereinigung 46 pp. 229-231, 1936 The first of two articles by Voderburg, in German. Four figures of Voderberg spiral tile, with one figure of the resultant spiral tiling.
————. ‘Zur Zerlegung der Ebene eines in kongruente Bereiche in Form einer Spirale’. Jahresbericht der Deutschen Mathematiker-Vereinigung 47 pp. 159-160, 1937 In German. Two figures of Voderburg spiral tile, but not shown as an actual tiling. Waldman, Cye H. ‘Voderberg Deconstructed & Triangle Substitution Tiling’ 2014. No article Much of interest; spiral tilings. Both popular and academic. Websites Crompton, Andrew http://www.cromp.com/pages/tess1.html Voderburg bird tiling. Ribault, Dominique. Polytess website Escher-like Elephant spiral tessellation. See notes |