Symmetries of Things

Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, together with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.
In this copiously illustrated treatise, Conway (mathematics, Princeton) and his colleagues explain the multifold world of symmetries. They begin with an introduction to symmetry starting with the repeating patterns in a kaleidoscope. The many visual examples help the reader in comprehending the methods the authors are using, many of which are a product of their own work. The chapters lead up to the "Magic Theorem" which demonstrates that plane repeating patterns comes in only seventeen types. From planes they move to spheres, folded patterns, Escher-like patterns and Klein bottles. They add the dimension of symmetry of colors to the mix, as well. A firm grounding in non-Euclidian geometry is necessary to truly understand this work but even non-mathematicians can glimpse the way in which the authors explain the symmetry all around us. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.