Beautiful Symmetry: A Coloring Book about Math

Beautiful Symmetry is a geometric coloring book that uses different coloring methods to introduce advanced mathematics. I recommend Beautiful Symmetry for anyone interested in the interplay between 2-dimensional geometric objects and advanced algebraic concepts. High school and early undergraduate students may find this book to be an interesting introduction to abstract algebra. Those who have some abstract algebra experience (advanced undergraduates and beyond) may enjoy applying their advanced knowledge to color the shapes presented in unique ways.  

 

Pages of repeated and changing patterns of triangles, circles, and swirls of all forms are mesmerizing.  The shapes beg for color. Questions and exercises lead one to create unique geometric configurations and develop mathematical intuition.

 

The first portion of the book focuses on introducing the concept of groups through symmetries of 2-dimensional shapes.  Both cyclic groups and dihedral groups are introduced.  Once there is a firm foundation of groups, subgroups are introduced by restricting symmetries using colors.  Of course, coloring is encouraged from the beginning of the book.  With a firm foundation of groups and subgroups, discussion begins on Frieze groups and translations.  The book ends with a classification of the wallpaper groups.

 

The only other widely available mathematics coloring book, that I am aware of, is Patterns of the Universe: A Coloring Adventure in Math and Beauty by Alex Bellos and Edmund Harriss. These two texts are quite different in theme.  Beautiful Symmetry uses the coloring and symmetries to introduce algebraic concepts, while Patterns of the Universe presents patterns to the reader and describes their mathematical significance.  

 

I strongly recommend this book to any artistic math-interested person looking for a new, physical, tangible, hypnotizing way to explore abstract algebra.

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Mckenzie West (westmr@uwec.edu) is an assistant professor at the University of Wisconsin - Eau Claire.  Her mathematical research is in the field of computational number theory and arithmetic geometry.