Tilings and patterns (book)

Tilings and patterns (book)
Name	Tilings and patterns
Author	Branko Grünbaum; Günter M. Shephard
Country	United Kingdom
Language	English language
Subject	Mathematics; Art
Genre	Reference
Publisher	W. H. Freeman and Company
Pub date	1987
Pages	696

Tilings and patterns (book) is a comprehensive monograph by Branko Grünbaum and Günter M. Shephard presenting systematic treatments of planar and spatial tilings, symmetry, and combinatorial aspects of tessellation. The book situates itself within traditions connected to Johannes Kepler, Albrecht Dürer, M. C. Escher, Benoît Mandelbrot and later developments in crystallography, serving both as a mathematical reference and an artistic sourcebook. It has been cited across literature associated with International Congress of Mathematicians, Royal Society, American Mathematical Society, Mathematical Association of America and museum catalogues.

Overview

The work offers a unified exposition linking classical studies by Euclid and Kepler to twentieth‑century research by Hermann Weyl, Harold Scott Macdonald Coxeter, Roger Penrose, Johannes Kepler (revisited), Roger Penrose (aperiodicity), and modern authors such as John Conway, Marjorie Rice, Martin Gardner, David Hilbert, Felix Klein and Eugenio Beltrami. It treats periodic, aperiodic, edge-to-edge and non-edge-to-edge tilings with reference to problems raised at gatherings like the International Congress on Mathematical Education and institutions including Smithsonian Institution and Victoria and Albert Museum. The book also cross-references research from laboratories such as Bell Labs and Los Alamos National Laboratory where computational experiments influenced tiling theory.

Publication history

Originally published in 1987 by W. H. Freeman and Company, the monograph followed earlier surveys and conference proceedings presented at venues like Mathematical Association of America meetings, workshops at Princeton University, and seminars hosted by Institute for Advanced Study. Subsequent reprints and distribution involved academic presses and university libraries such as Harvard University Press and Cambridge University Press collections. Editions were used in courses at Massachusetts Institute of Technology, University of California, Berkeley, Oxford University and Cambridge University.

Content and structure

Chapters organize material on tiling theory, combinatorial tilings, symmetry groups, and substitution systems, referencing foundational work by E. S. Fedorov, George Pólya, Aleksandr Aleksandrovich (as part of geometric tradition), Richard P. Feynman (for physical analogies) and Linus Pauling (for crystal motifs). The structure includes formal definitions, classification theorems, enumeration techniques, and exercises connected to problems posed at International Mathematical Olympiad style competitions and research problems circulated via Mathematical Reviews. Detailed treatments examine wallpaper groups with nods to Bieberbach theorem-related developments and links to investigations at National Institute of Standards and Technology.

Illustrations and design

Illustrations draw on classical ornamentation from collections at the Metropolitan Museum of Art, designs by M. C. Escher, sketches reminiscent of Albrecht Dürer and diagrams used by Harold Scott Macdonald Coxeter in lectures. Plates demonstrate tilings found in Islamic art from Alhambra, mosaics studied at Pompeii, and patterns employed in Buckminster Fuller experiments, while technical figures invoke imagery from crystallographic atlases curated at Royal Institution and drawings used by William Rowan Hamilton and August Möbius.

Reception and impact

The book received attention in reviews published by journals associated with American Mathematical Society, Mathematical Gazette, Nature (journal), Science (journal), and writings in magazines linked to Smithsonian Institution. Scholars including John Conway, Roger Penrose, Maryam Mirzakhani (in thematic contexts), Timothy Gowers and editors at Cambridge University Press have noted its encyclopedic scope. It influenced exhibitions at Victoria and Albert Museum and pedagogical approaches in programs at Royal College of Art and Rhode Island School of Design.

Editions and translations

Following the first edition, subsequent printings and a second revised edition were issued, and translations appeared for audiences tied to institutions such as École Normale Supérieure, École Polytechnique, Technische Universität München, Università di Roma, Kyoto University and Peking University. Academic catalogs and libraries including Library of Congress and British Library list multiple holdings. Reprints and facsimiles coordinated with publishers linked to Oxford University Press and regional academic publishers increased its international reach.

Influence on mathematics and art

The monograph shaped research programs in aperiodic order, influenced work by Roger Penrose and Alan Gardiner (in crystallography contexts), and informed computational explorations at IBM and MIT Media Lab. Its cross-disciplinary impact appears in studies by curators at Museum of Modern Art, in designs adopted by studios collaborating with Zaha Hadid Architects, and in scientific literature on quasicrystals tied to Shechtman Nobel Prize-era discoveries. The book remains cited in contemporary research connecting tiling theory to topics addressed at International Congress of Mathematicians and symposia organized by European Mathematical Society.

Category:Mathematics books Category:Art books