The Symmetries of Things
by Conway ,John H.Format: Hardcover
Pub. Date: 2008-04-18
Publisher(s): TAYLOR & FRANCIS
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Summary
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.
Table of Contents
| Figure Acknowledgments | |
| Symmetries of Finite Objects and Plane Repeating Patterns | p. 1 |
| Symmetries | p. 7 |
| Planar Patterns | p. 15 |
| The Magic Theorem | p. 29 |
| The Spherical Patterns | p. 51 |
| Frieze Patterns | p. 67 |
| Why the Magic Theorems Work | p. 75 |
| Euler's Map Theorem | p. 83 |
| Classification of Surfaces | p. 93 |
| Orbifolds | p. 109 |
| Color Symmetry, Group Theory, and Tilings | p. 117 |
| Presenting Presentations | p. 125 |
| Twofold Colorations | p. 135 |
| Threefold Colorings of Plane Patterns | p. 153 |
| Other Primefold Colorings | p. 161 |
| Searching for Relations | p. 171 |
| Types of Tilings | p. 185 |
| Abstract Groups | p. 199 |
| Repeating Patterns in Other Spaces | p. 215 |
| Introducing Hyperbolic Groups | p. 219 |
| More on Hyperbolic Groups | p. 231 |
| Archimedean Tilings | p. 251 |
| Generalized Schlafli Symbols | p. 269 |
| Naming Archimedean and Catalan Polyhedra and Tilings | p. 283 |
| The 35 "Prime" Space Groups | p. 301 |
| Objects with Prime Symmetry | p. 327 |
| Flat Universes | p. 355 |
| The 184 Composite Space Groups | p. 367 |
| Higher Still | p. 383 |
| Other Notations For the Plane and Spherical Groups | p. 415 |
| Bibliography | p. 419 |
| Index | p. 423 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
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