Beautiful Symmetry: A Coloring Book about Math

by Alex Berke, Alex Bellos (Foreword by)

Overview

A coloring book that invites readers to explore symmetry and the beauty of math visually.

Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts.

Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them.

Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

Product Details

ISBN-13:	9780262538923
Publisher:	MIT Press
Publication date:	02/18/2020
Series:	The MIT Press
Pages:	168
Product dimensions:	6.90(w) x 8.90(h) x 0.60(d)
Age Range:	18 - 12 Years

About the Author

Alex Berke is currently at the MIT Media Lab. She previously worked as a technologist, most recently as a software engineer at Google.

Table of Contents

Foreword Alex Bellos

Part I Shapes & Symmetries

Introduction 2

Rotations 6

Counting rotations 6

Cyclic groups 13

Generators 17

Subgroups and group closure 24

Reflections 33

Seeing and generating mirrors 33

Dihedral groups 37

Subgroups of dihedral groups 44

Inverses 52

Part II Infinitely Repeating Patterns

Frieze Groups 60

Infinite repetition and translations 60

Mirrors, rotations, glide reflections 65

Patterns as illustrations of groups 74

Combining symmetries 78

Wallpaper Groups 88

Infinite repetitions in two dimensions 90

Possible rotations 95

Exploration of pattern groups and symmetries 103

With extra challenges and illustrations Conclusion 136

Notes on Notation

Theory Reference

Challenge Solutions & More

What People are Saying About This

From the Publisher

“This glorious book works on many levels: as a pure picture book giving an introduction into the world of mathematical beauty, as a visual introduction to the ideas of group theory, as an interactive coloring book, or as a book of patterns to admire. This is deep math without numbers, equations, or answers. It is an invitation to feel math, viscerally, as a starting point or as an end in itself.”

—Eugenia Cheng, Author of The Art of Logic in an Illogical World