# Creating Symmetry: The Artful Mathematics of Wallpaper Patterns by Frank A. Farris (Hardback, 2015)

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- Author(s)Frank A. Farris
- PublisherPrinceton University Press
- Date of Publication02/06/2015
- Language(s)English
- FormatHardback
- ISBN-100691161739
- ISBN-139780691161730
- GenrePopular Science

- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note103 color illus.

- Weight1021 g
- Width229 mm
- Height254 mm
- Pagination248

- 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 229
- Author BiographyFrank 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.
- PrizesCommended for PROSE Award in Mathematics, Association of American Publishers 2016.

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