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The Symmetries of Things

Hal Harris's picture
Sun, 03/01/2009 - 00:00 -- Hal Harris

This beautiful book could certainly enhance your coffee table, but don't buy it just for its looks. Be prepared to spend some time with it, and join the wonder that mathematicians are expressing at the brilliance of this new way of describing and inventing symmetries. "The Symmetries of Things" begins with a classification of the elements of symmetry - the orbifold signature notation, whose features are "wonders, gyrations, kaleidoscopes, and miracles". Combined, they give the "signature" of a pattern. There is a Magic Theorem that tells you how features can be combined. John Conway may be known to you from his cellular automaton "Game of Life" and the puzzles and amusements that have been described by Martin Gardner. His coauthors are a former graduate student (Burgiel) and Goodman-Strauss, who is a mathematician whose exceptionally beautiful illustrations are widely-known. More than twenty years in the making, the book is divided into three parts. The first should be accessible to lay readers who may be lured into mathematical ideas before they realize it. Part two introduces color to symmetry and requires some understanding of group theory (and was more than sufficiently challenging to this physical chemist). Part three is intended only for professional mathematicians and goes into symmetries in higher dimensions. I do not see exactly how this is relevant to chemistry, but I would not be surprised if it finds application in supramolecular chemistry and self-organization.

Pick Attribution: 

John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss

Publication Date: 
Tuesday, January 1, 2008