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When most of us think of symmetry, we think of looking into a mirror or playing patty-cake with a child. As Oxford don du Sautoy (The Music of the Primes) tells readers, this is only the tip of the triangle in the mathematical realms of symmetry, where symmetrical objects exist in dimensions far beyond our ability to imagine. The author takes readers gently by the hand and leads them elegantly through some steep and rocky terrain as he explains the various kinds of symmetry and the objects they swirl around. Du Sautoy explains how this twirling world of geometric figures has strange but marvelous connections to number theory, and how the ultimate symmetrical object, nicknamed "the Monster," is related to string theory. This book is also a memoir in which du Sautoy describes a mathematician's life and how one makes a discovery in these strange lands. He also blends in minibiographies of famous figures like Galois, who played significant roles in this field. This is mainly for science buffs, but fans of scientific biographies will also find it appealing. B&w illus. (Mar.) Copyright 2007 Reed Business Information.