Robert Fathauer

Tessellations (eBook, PDF)

Mathematics, Art, and Recreation

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 464
• Erscheinungstermin: 7. Dezember 2020
• Englisch
• ISBN-13: 9780429591174
• Artikelnr.: 60394335

Autorenporträt

Robert Fathauer has had a life-long interest in art but studied physics and mathematics in college, going on to earn a PhD from Cornell University in electrical engineering. For several years he was a researcher at the Jet Propulsion Laboratory in Pasadena, California. Long a fan of M.C. Escher, he began designing his own tessellations with lifelike motifs in the late 1980s. In 1993, he founded a business, Tessellations, to produce puzzles based on his designs. Over time, Tessellations has grown to include mathematics manipulatives, polyhedral dice, and books.
Dr. Fathauer's mathematical art has always been coupled with recreational math explorations. These include Escheresque tessellations, fractal tilings, and iterated knots. After many years of creating two-dimensional art, he has recently been building ceramic sculptures inspired by both mathematics and biological forms. Another interest of his is photographing mathematics in natural and synthetic objects, particularly tessellations. In addition to creating mathematical art, he's strongly committed to promoting it through group exhibitions at both the Bridges Conference and the Joint Mathematics Meetings.

Inhaltsangabe

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.