The Tiling Book: An Introduction to the Mathematical Theory of Tilings

by Colin Adams

Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there is both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

298 pages, Hardcover

Published August 17, 2022

About the author

A Game Artist and Illustrator, Colin Adams works with pencils, brushes, pens, and digital styluses. Colin lives and works in the San Francisco Bay Area in California. His clients range the world of illustration, and include books, magazines, social and mobile games, storyboards, web sites, roleplaying games, and comic books. He has drawn his entire life. He drew a lot in art school, and spent most of his regular school years drawing on his math homework anyway. He has some influences, a few pets, likes avocados, dislikes pennies, and he really couldn’t pick a favorite color, even when pressed.

Reviews

[Wisconsin Alumni]

Colin Adams MA’80, PhD’83
Author

From the author:
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.