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.
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Editorial Reviews
Review
This book is a plaything, an inexhaustible exercise in brain expansion for the reader, a work of art and a bold statement of what the culture of math can be like, all rolled into one. Like any masterpiece, The Symmetries of Things functions on a number of levels simultaneously… . It is imperative to get this book into the hands of as many young mathematicians as possible. And then to get it into everyone else's hands. --American Scientist
This book gives a refreshing and comprehensive account of the subject of symmetry--subject that has fascinated humankind for centuries… . Overall, the book is a treasure trove, full of delights both old and new. Much of it should be accessible for anyone with an undergraduate-level background in mathematics, and is likely to stimulate further interest. --Mathematical Reviews
Conway, Burgiel, and Goodman-Strauss have written a wonderful book which can be appreciated on many levels. … [M]athematicians and math-enthusiasts at a wide variety of levels will be able to learn some new mathematics. Even better, the exposition is lively and engaging, and the authors find interesting ways of telling you the things you already know in addition to the things you don't. --MAA Reviews
This book gives a refreshing and comprehensive account of the subject of symmetry--subject that has fascinated humankind for centuries… . Overall, the book is a treasure trove, full of delights both old and new. Much of it should be accessible for anyone with an undergraduate-level background in mathematics, and is likely to stimulate further interest. --Mathematical Reviews
Conway, Burgiel, and Goodman-Strauss have written a wonderful book which can be appreciated on many levels. … [M]athematicians and math-enthusiasts at a wide variety of levels will be able to learn some new mathematics. Even better, the exposition is lively and engaging, and the authors find interesting ways of telling you the things you already know in addition to the things you don't. --MAA Reviews
About the Author
John H. Conway is the John von Neumann Chair of Mathematics at Princeton University. He obtained his BA and his PhD from the University of Cambridge (England). He is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the Game of Life.
Heidi Burgiel is a professor in the Department of Mathematics and Computer Science at Bridgewater State College. She obtained her BS in Mathematics from MIT and her PhD in Mathematics from the University of Washington. Her primary interests are educational technology and discrete geometry.
Chaim Goodman-Strauss is a professor in the department of mathematical sciences at the University of Arkansas. He obtained both his BS and PhD in Mathematics at the University of Texas at Austin. His research interests include low-dimensional topology, discrete geometry, differential geometry, the theory of computation, and mathematical illustration. Since 2004 he has been broadcasting mathematics on a weekly radio segment.
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Most Helpful Customer Reviews
34 of 36 people found the following review helpful:
5.0 out of 5 stars
Exquisite and fascinating and informative,
By rbnn (Berkeley, CA United States) - See all my reviews
Amazon Verified Purchase(What's this?)
This review is from: The Symmetries of Things (Hardcover)
Fascinating and thrilling take on finite groups, presented by means of planar and higher-dimensional symmetries.
Presentation will be clear and interesting to laypersons and to mathematicians. Three features distinguish this book from other discussions of symmetry. First is the inherent interest in the subject. Symmetry is a topic of much greater importance and pervasiveness than most people realize. This book helps us see it in many places we might not think to look, and its classification and analysis is extremely informative and thought-provoking. Second is the beauty of the examples, which deal with elegant and attractive patterns. Third is the extraordinarily high production values of the book. The notation for symmetry utilizes different colors in a way that is clear and helpful. The pictures are carefully done. Frankly, this is one of the most beautiful books I've ever owned. My one complaint is that the corner of the cover of the copy I got from Amazon was a bit bent. It seems like too much trouble to ship it back and get a whole new copy for this, since the text is fine. This is quite unusual for Amazon, however. In any case, I highly recommend this book for anyone interested in mathematics or even in art, from curious high school students to professional mathematicians.
12 of 13 people found the following review helpful:
4.0 out of 5 stars
good summary but tough going,
By
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This review is from: The Symmetries of Things (Hardcover)
This book provides a very detailed overview of two and three dimensional symmetry types, but for the non-mathematician it can be tough going as the book progresses.
18 of 46 people found the following review helpful:
5.0 out of 5 stars
Even the most basic of things can be beautiful,
By Midwest Book Review (Oregon, WI USA) - See all my reviews
This review is from: The Symmetries of Things (Hardcover)
One of the most base concepts of art - symmetry. "The Symmetries of Things" is a guide to this most basic concept showing that even the most basic of things can be beautiful - and addresses why the simplest of patterns mesmerize humankind and the psychological and mathematical importance of symmetry in one's every day life. "The Symmetries of Things" is an intriguing book from first page to last, highly recommended to the many collections that should welcome it.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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threefold colorings, kaleidoscopic points, normal cubic lattice, octad group, gyration points, frieze patterns, tetrad group, four fundamental features, chiral part, snub cube, spherical patterns, polyhedral groups, face code, spherical groups, hyperbolic groups, plenary groups, placement code, truncated octahedra, rhombic dodecahedra, duality groups, topological disk, plane patterns, planar patterns, generic presentation, mirror lines Key Phrases - Capitalized Phrases (CAPs): (learn more)
Generalized Schläfli Symbols, Euler's Theorem, Naming Arch, Symmetry Work, Isohedral Types, Archimedean Tilings, The Voronoi, Ath Prime Symmetry, Higher Still, Where Are, Circle Limit, Types of Things, Proof of the Inequivalence Theorem, Other Primefold Colorings, Space Croups, Twofold Colorations, Magic Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
threefold colorings, kaleidoscopic points, normal cubic lattice, octad group, gyration points, frieze patterns, tetrad group, four fundamental features, chiral part, snub cube, spherical patterns, polyhedral groups, face code, spherical groups, hyperbolic groups, plenary groups, placement code, truncated octahedra, rhombic dodecahedra, duality groups, topological disk, plane patterns, planar patterns, generic presentation, mirror lines Key Phrases - Capitalized Phrases (CAPs): (learn more)
Generalized Schläfli Symbols, Euler's Theorem, Naming Arch, Symmetry Work, Isohedral Types, Archimedean Tilings, The Voronoi, Ath Prime Symmetry, Higher Still, Where Are, Circle Limit, Types of Things, Proof of the Inequivalence Theorem, Other Primefold Colorings, Space Croups, Twofold Colorations, Magic Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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