Tessellations: Mathematics, Art, and Recreation

ISBN-13: 9780367185978 / Angielski / Twarda / 2020 / 464 str.

Robert Fathauer

Opis

This book aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. It covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Also includes special topics like spiral tilings and tessellation metamorphoses.

 

Spis treści

1. Introduction to Tessellations.  2. Geometric Tessellations.  3. Symmetry and Transformations in Tessellations.  4. Tessellations in Nature.  5. Decorative and Utilitarian Tessellations.  6. Polyforms and Reptiles.  7. Rosettes and Spirals.  8. Matching Rules, Aperiodic Tiles, and Substitution Tilings.  9. Fractal Tiles and Fractal Tilings.  10. Non-Euclidean Tessellations.  11. Tips on Designing and Drawing Escheresque Tessellations.  12. Special Techniques to Solve Design Problems.  13. Escheresque Tessellations Based on Squares.  14. Escheresque Tessellations Based on Isosceles Right Triangle and Kite-Shaped Tiles.  15. Escheresque Tessellations Based on Equilateral Triangle Tiles.  16. Escheresque Tessellations Based on 60°–120° Rhombus Tiles.  17. Escheresque Tessellations Based on Hexagonal Tiles.  18. Decorating Tiles to Create Knots and Other Designs.  19. Tessellation Metamorphoses and Dissections.  20. Introduction to Polyhedra.  21. Adapting Plane Tessellations to Polyhedra.  22. Tessellating the Platonic Solids.  23. Tessellating the Archimedean Solids. 24. Tessellating Other Polyhedra. 25. Tessellating Other Surfaces.