Tessellations: Mathematics, Art, and Recreation

by Robert Fathauer

Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. Additionally, it covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Inclusion of special topics like spiral tilings and tessellation metamorphoses allows the reader to explore beautiful and entertaining math and art.

The book has a particular focus on ‘Escheresque’ designs, in which the individual tiles are recognizable real-world motifs. These are extremely popular with students and math hobbyists but are typically very challenging to execute. Techniques demonstrated in the book are aimed at making these designs more achievable. Going beyond planar designs, the book contains numerous nets of polyhedra and templates for applying Escheresque designs to them.

Activities and worksheets are spread throughout the book, and examples of real-world tessellations are also provided.

Key features



Introduces the mathematics of tessellations, including symmetry

Covers polygonal, aperiodic, and non-Euclidean tilings

Contains tutorial content on designing and drawing Escheresque tessellations

Highlights numerous examples of tessellations in the real world

Activities for individuals or classes

Filled with templates to aid in creating Escheresque tessellations

Treats special topics like tiling rosettes, fractal tessellations, and decoration of tiles

464 pages, Kindle Edition

Published December 7, 2020

Reviews

[Riley White · Rating 5 out of 5]

This was a very nice book, and definitely worth picking up for anyone interested in tilings. Note that it is not a math textbook: there are no theorems, proofs, or exercises (although there are small activities intended for use in a classroom setting). Those primarily interested in theory should therefore look elsewhere, although this book would still probably be a useful companion. Most of the book is something like an encyclopedia of interesting tilings, some ways of classifying them, and different methods of producing interesting tilings, along with a small amount of more applied material thrown in. There is also a large section, maybe a bit less than half (although perhaps inflated due to the many full page templates), focused on creating physical Escheresque tilings and tessellated polyhedra. This latter material makes the book particularly valuable for those interested in the artistic aspects of tessellations.