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Awards
OverviewThis lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks--a sort of potato-stamp method--Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry.Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book. Full Product DetailsAuthor: Frank A. FarrisPublisher: Princeton University Press Imprint: Princeton University Press Dimensions: Width: 22.90cm , Height: 2.50cm , Length: 25.40cm Weight: 1.021kg ISBN: 9780691161730ISBN 10: 0691161739 Pages: 248 Publication Date: 02 June 2015 Audience: General/trade , College/higher education , General , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Language: English Table of ContentsPreface vii 1 Going in Circles 1 2 Complex Numbers and Rotations 5 3 Symmetry of the Mystery Curve 11 4 Mathematical Structures and Symmetry: Groups, Vector Spaces, and More 17 5 Fourier Series: Superpositions of Waves 24 6 Beyond Curves: Plane Functions 34 7 Rosettes as Plane Functions 40 8 Frieze Functions (from Rosettes!) 50 9 Making Waves 60 10 PlaneWave Packets for 3-Fold Symmetry 66 11 Waves, Mirrors, and 3-Fold Symmetry 74 12 Wallpaper Groups and 3-Fold Symmetry 81 13 ForbiddenWallpaper Symmetry: 5-Fold Rotation 88 14 Beyond 3-Fold Symmetry: Lattices, Dual Lattices, andWaves 93 15 Wallpaper with a Square Lattice 97 16 Wallpaper with a Rhombic Lattice 104 17 Wallpaper with a Generic Lattice 109 18 Wallpaper with a Rectangular Lattice 112 19 Color-ReversingWallpaper Functions 120 20 Color-Turning Wallpaper Functions 131 21 The Point Group and Counting the 17 141 22 Local Symmetry in Wallpaper and Rings of Integers 157 23 More about Friezes 168 24 Polyhedral Symmetry (in the Plane?) 172 25 HyperbolicWallpaper 189 26 Morphing Friezes and Mathematical Art 200 27 Epilog 206 A Cell Diagrams for the 17 Wallpaper Groups 209 B Recipes forWallpaper Functions 211 C The 46 Color-ReversingWallpaper Types 215 Bibliography 227 Index 229ReviewsHonorable Mention for the 2016 PROSE Award in Mathematics, Association of American Publishers [A] beautifully illustrated guide to fusing mathematical and artistic creativity to generate fascinating and visually appealing designs. --Evelyn Lamb, Scientific American [A] beautiful book... [Creating Symmetry] is a thoughtful, innovative and interesting piece of work, discussing material that the author is obviously very enthusiastic about; such enthusiasm is, as is often the case, contagious. --Mark Hunacek, MAA Reviews This is a marvelous book that brings groups, and along the way many other mathematical concepts, to the reader in an unconventional way. --Adhemar Bultheel, European Mathematical Society Bulletin Mathematics students thus get a visually rich path into group theory that compellingly informs even first steps with ideas usually deemed advanced. Braver art students will find motivation and the means to learn some mathematics they can put right to use. --D. V. Feldman, Choice [A] delightful showcase of artistic applications of complex wave functions. . . . This attractive book will appeal to and inspire a broad range of practitioners including complex analysts, mathematical artists, and advanced undergraduates. --Heidi Burgiel, College Mathematics Journal Mathematics students thus get a visually rich path into group theory that compellingly informs even first steps with ideas usually deemed advanced. Braver art students will find motivation and the means to learn some mathematics they can put right to use. --D. V. Feldman, Choice This is a marvelous book that brings groups, and along the way many other mathematical concepts, to the reader in an unconventional way. --Adhemar Bultheel, European Mathematical Society Bulletin [A] beautiful book. . . . [Creating Symmetry] is a thoughtful, innovative and interesting piece of work, discussing material that the author is obviously very enthusiastic about; such enthusiasm is, as is often the case, contagious. --Mark Hunacek, MAA Reviews [A] beautifully illustrated guide to fusing mathematical and artistic creativity to generate fascinating and visually appealing designs. --Evelyn Lamb, Scientific American Honorable Mention for the 2016 PROSE Award in Mathematics, Association of American Publishers [A] beautiful book... [Creating Symmetry] is a thoughtful, innovative and interesting piece of work, discussing material that the author is obviously very enthusiastic about; such enthusiasm is, as is often the case, contagious. --Mark Hunacek, MAA Reviews Author InformationFrank A. Farris teaches mathematics at Santa Clara University. He is a former editor of Mathematics Magazine, a publication of the Mathematical Association of America. He lives in San Jose, California. 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