Creating Symmetry: The Artful Mathematics of Wallpaper Patterns

Title\nCopyright\nContents\nPreface\n1 Going in Circles\n2 Complex Numbers and Rotations\n3 Symmetry of the Mystery Curve\n4 Mathematical Structures and Symmetry: Groups, Vector Spaces, and More\n5 Fourier Series: Superpositions of Waves\n6 Beyond Curves: Plane Functions\n7 Rosettes as Plane Functions\n8 Frieze Functions (from Rosettes!)\n9 Making Waves\n10 Plane Wave Packets for 3-Fold Symmetry\n11 Waves, Mirrors, and 3-Fold Symmetry\n12 Wallpaper Groups and 3-Fold Symmetry\n13 Forbidden Wallpaper Symmetry: 5-Fold Rotation\n14 Beyond 3-Fold Symmetry: Lattices, Dual Lattices, and Waves\n15 Wallpaper with a Square Lattice\n16 Wallpaper with a Rhombic Lattice\n17 Wallpaper with a Generic Lattice\n18 Wallpaper with a Rectangular Lattice\n19 Color-Reversing Wallpaper Functions\n20 Color-Turning Wallpaper Functions\n21 The Point Group and Counting the 17\n22 Local Symmetry in Wallpaper and Rings of Integers\n23 More about Friezes\n24 Polyhedral Symmetry (in the Plane?)\n25 Hyperbolic Wallpaper\n26 Morphing Friezes and Mathematical Art\n27 Epilog\nA Cell Diagrams for the 17 Wallpaper Groups\nB Recipes for Wallpaper Functions\nC The 46 Color-ReversingWallpaper Types\nBibliography\nIndex