''Tilings and patterns'' is a book by mathematicians
Branko Grünbaum
Branko Grünbaum (; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descentGeoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed.
Structure and topics
The book is concerned with tilings—a partition of the plane into regions (the tiles)—and
pattern
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated l ...
s—repetitions of a motif in the plane in a regular manner.
The book is divided into two parts. The first seven chapters define concepts and terminology, establish the general theory of tilings, survey tilings by regular
polygon
In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain.
The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
s, review the theory of patterns, and discuss tilings in which all the tiles, or all the edges, or all the vertices, play the same role.
The last five chapters survey a variety of advanced topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings,
Wang tile
Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, is a class of formal systems. They are modeled visually by square tiles with a color on each side. A set of such tiles is selected, and ...
s, and tilings with unusual kinds of tiles.
Each chapter open with an introduction to the topic, this is followed by the detailed material of the chapter, much previously unpublished, which is always profusely illustrated, and normally includes examples and proofs. Chapters close with exercises, and a section of notes and references which detail the historical development of the topic. These notes sections are interesting and entertaining, as they discuss the efforts of the previous workers in the field and detail the good (and bad) approaches to the topic. The notes also identify unsolved problems, point out areas of potential application, and provide connections to other disciplines in mathematics, science, and the arts.
The book has 700 pages, including a 40-page, 800-entry bibliography, and an index. The book is used as a source on numerous Wikipedia pages.
Audience
In their preface the authors state "We have written this book with three main groups of readers in mind—students, professional mathematicians and non-mathematicians whose interests include patterns and shapes (such as artists, architects, crystallographers and others).Grünbaum, B. and Shephard, G.C. (1987). ''Tilings and patterns'', W.H. Freeman, New York, 700pp. ,
Other reviewers commented as follows:
* "The most striking feature of the book is its extensive collection of figures, including hundreds of examples of tilings and patterns. The sheer abundance is perhaps one reason why artists and designers have been drawn to it over the years."Satzer, W.J. (2016) Tilings and patterns MAA Reviews.
* "Their idea was that the book should be accessible to any reader who is attracted to geometry."Roman, T. (1988). ''Revue des publications'', Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, Nouvelle Série, 32 (80), No. 4, 379-380.
Reception
Contemporary reviews of the book were overwhelming positive. The book was reviewed by 15 journals in the fields of crystallography, mathematics, and the sciences. Quotations from major reviews:
Influence
The book was praised in later journal articles by multiple authors:
The book was also praised in later books by other authors:
Editions
* The hardback original ''Tilings and patterns'' was published in 1987.
* ''Tilings and patterns - an introduction'', a paperback reprint of the first seven chapters of the 1987 original, was published in 1989.
* In 2016 a second edition of the full text was published by
Dover
Dover ( ) is a town and major ferry port in Kent, southeast England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies southeast of Canterbury and east of Maidstone. ...
in paperback, with a new preface and an appendix describing progress in the subject since the first edition.Grünbaum, B. and Shephard, G.C. (2016) ''Tilings and patterns'', 2nd ed., Dover, Mineola NY, 710pp. , The reviewer at '' MAA Reviews'' commented "Dover has once again done the mathematical community a service in bringing back such a notable volume."
References
External links
* ' at the
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...