Creating Symmetry : The Artful Mathematics of Wallpaper Patterns

Frontmatter -- Contents -- Preface -- 1. Going in Circles -- 2. Complex Numbers and Rotations -- 3. Symmetry of the Mystery Curve -- 4. Mathematical Structures and Symmetry: Groups, Vector Spaces, and More -- 5. Fourier Series: Superpositions of Waves -- 6. Beyond Curves: Plane Functions -- 7. Roset...
Ausführliche Beschreibung

Frontmatter -- Contents -- Preface -- 1. Going in Circles -- 2. Complex Numbers and Rotations -- 3. Symmetry of the Mystery Curve -- 4. Mathematical Structures and Symmetry: Groups, Vector Spaces, and More -- 5. Fourier Series: Superpositions of Waves -- 6. Beyond Curves: Plane Functions -- 7. Rosettes as Plane Functions -- 8. Frieze Functions (from Rosettes!) -- 9. Making Waves -- 10. Plane Wave Packets for 3-Fold Symmetry -- 11. Waves, Mirrors, and 3-Fold Symmetry -- 12. Wallpaper Groups and 3-Fold Symmetry -- 13. Forbidden Wallpaper Symmetry: 5-Fold Rotation -- 14. Beyond 3-Fold Symmetry: Lattices, Dual Lattices, and Waves -- 15. Wallpaper with a Square Lattice -- 16. Wallpaper with a Rhombic Lattice -- 17. Wallpaper with a Generic Lattice -- 18. Wallpaper with a Rectangular Lattice -- 19. Color-Reversing Wallpaper Functions -- 20. Color-Turning Wallpaper Functions -- 21. The Point Group and Counting the 17 -- 22. Local Symmetry in Wallpaper and Rings of Integers -- 23. More about Friezes -- 24. Polyhedral Symmetry (in the Plane?) -- 25. Hyperbolic Wallpaper -- 26. Morphing Friezes and Mathematical Art -- 27. Epilog -- A. Cell Diagrams for the 17 Wallpaper Groups -- B. Recipes for Wallpaper Functions -- C. The 46 Color-Reversing Wallpaper Types -- Bibliography -- Index Ausführliche Beschreibung