Creating Symmetry: The Artful Mathematics of Wallpaper PatternsA step-by-step illustrated introduction to the astounding mathematics of symmetry |
Contents
1 | |
5 | |
11 | |
Groups Vector Spaces and More | 17 |
Superpositions of Waves | 24 |
Plane Functions | 34 |
7 Rosettes as Plane Functions | 40 |
8 Frieze Functions from Rosettes | 50 |
18 Wallpaper with a Rectangular Lattice | 112 |
19 ColorReversing Wallpaper Functions | 120 |
20 ColorTurning 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 Hyperbolic Wallpaper | 189 |
9 Making Waves | 60 |
10 Plane Wave Packets for 3Fold Symmetry | 66 |
11 Waves Mirrors and 3Fold Symmetry | 74 |
12 Wallpaper Groups and 3Fold Symmetry | 81 |
5Fold Rotation | 88 |
Lattices Dual Lattices and Waves | 93 |
15 Wallpaper with a Square Lattice | 97 |
16 Wallpaper with a Rhombic Lattice | 104 |
17 Wallpaper with a Generic Lattice | 109 |
26 Morphing Friezes and Mathematical Art | 200 |
27 Epilog | 206 |
A Cell Diagrams for the 17 Wallpaper Groups | 209 |
B Recipes for Wallpaper Functions | 211 |
C The 46 ColorReversingWallpaper Types | 215 |
227 | |
229 | |
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Creating Symmetry: The Artful Mathematics of Wallpaper Patterns Frank A. Farris Limited preview - 2015 |