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Symmetry: A Mathematical Exploration

Kristopher Tapp
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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Symmetry is a very useful concept in mathematics education, since it is an idea that young children can understand, yet that can form the basis of very sophisticated mathematics. The set of actions that can be performed on geometric figures is the best way to introduce group theory and with so many examples of symmetry in the natural world, it can be used in natural science classes as well.

In this book Tapp uses a large number of high-quality colored images to illustrate various properties derived from symmetry as well as to introduce students to the supporting mathematics, such as group theory, graph theory, vector operations and matrices. The level of difficulty is such that all mathematics undergraduates and most K–12 teachers of math and science will understand.

In many ways, this book could serve as a vital resource for teachers of children as they try to get young minds interested in learning mathematics. Exploring symmetry is one way children can learn math without realizing that they are in fact learning math; of course, the same applies to adults. Inexpensive manipulatives can be cut from heavy construction paper, so each child can physically work through and observe the operations. A set of problems is included at the end of each chapter, but solutions are not included.

The great thing about symmetry is that you need no endowment of math genes in order to understand it and perform the operations. This book is an excellent text for math courses for non-math majors, as it will teach them math without seeming to do so. Artists, in particular, will find a great deal that they can apply in their work.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.