Exploring Symmetry Coloring Book

I recently published a new book and it is not the one that I have been working on for the past five months. Rather it is an offshoot from that book.

In the process of working on the still uncompleted book, I realized I needed to get much more comfortable with symmetry. Mathematicians have shown that there are only 17 groups of two-dimensional symmetry in patterns that periodically repeat in more than one direction. My way of getting familiar with these 17 groups was to review the patterns that I have used to make mazes and classify them by group. Making a book ("writing a book" is not an accurate description of the process) organized my exploration of the topic and the coloring book format was quick and easy. As I worked on sorting patterns into groups, I developed additional patterns and some of these are included in the book. The title is Exploring Symmetry Coloring Book and the book is available from Amazon and CreateSpace with a list price of $5.99.

The book starts with six pages that give a short explanation of each of the 17 symmetry groups with feet used to illustrate the patterns. This is how feet illustrates the p31m group:

 p31m is one of the more difficult groups to identify because there is another group with very similar symmetry called p3m1.  Both groups repeat themselves if rotated 120 degrees around their centers of rotation and both have mirror reflection.

Below feet illustrate a group called p4g. It needs to be distinguished from a group called p4m.

 After the short introduction explaining how one can identify groups of symmetry, the book has almost 100 pages of patterns that can be colored or decorated. The pages may also inspire or help readers to create new designs and patterns.

I designed a maze book with a railroad theme and used the pattern of rails shown below for a maze. It has reflection symmetry around both vertical and horizontal lines. It can reproduce itself it rotated 180 degrees. Finally, it has a staggered pattern that is caused by what is called glide reflection.The group that has these attributes is called cmm.

In designing a book of pirate mazes, I used a pattern with swords. In working on this book I found several other ways to use swords in patterns, such as this one which is p3. A benefit of working out thoughts in a book form is that it led to new patterns.

I tried to limit the number of designs that are fairly well known though I have used quite a number of them in mazes. The one below I found years ago in Tilings and Patterns by Branko Grunbaum and Geoffrey Shepard, It is another example of p4g.

There are other coloring books of geometrical and symmetrical designs that feature more complex and intricate designs and are probably better choices for those who want only a coloring book. Exploring Symmetry Coloring Book is not only a coloring book, it is also an introduction to the topic of symmetry. It is an educational coloring book.

Although young children can color the pages, only older people will appreciate the explanation of the symmetry groups. Supplementing the introduction, there is a page of notes at the end that identifies the groups used on each page.

Available from Amazon and Create Space.