Chapter 5. Euclid and His “Elements”

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface ix
4. Introduction 1
5. Chapter 1. Leonhard Euler and His Three “Great” Friends 10
6. Chapter 2. What Is a Polyhedron? 27
7. Chapter 3. The Five Perfect Bodies 31
8. Chapter 4. The Pythagorean Brotherhood and Plato’s Atomic Theory 36
9. Chapter 5. Euclid and His “Elements” 44
10. Chapter 6. Kepler’s Polyhedral Universe 51
11. Chapter 7. Euler’s Gem 63
12. Chapter 8. Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes 75
13. Chapter 9. Scooped by Descartes? 81
14. Chapter 10. Legendre Gets It Right 87
15. Chapter 11. A Stroll through Königsberg 100
16. Chapter 12. Cauchy’s Flattened Polyhedra 112
17. Chapter 13. Planar Graphs, Geoboards, and Brussels Sprouts 119
18. Chapter 14. It’s a Colorful World 130
19. Chapter 15. New Problems and New Proofs 145
20. Chapter 16. Rubber Sheets, Hollow Doughnuts, and Crazy Bottles 156
21. Chapter 17. Are They the Same, or Are They Different? 173
22. Chapter 18. A Knotty Problem 186
23. Chapter 19. Combing the Hair on a Coconut 202
24. Chapter 20. When Topology Controls Geometry 219
25. Chapter 21. The Topology of Curvy Surfaces 231
26. Chapter 22. Navigating in n Dimensions 241
27. Chapter 23. Henri Poincaré and the Ascendance of Topology 253
28. Epilogue: The Million-Dollar Question 265
29. Acknowledgments 271
30. Appendix A. Build Your Own Polyhedra and Surfaces 273
31. Appendix B. Recommended Readings 283
32. Notes 287
33. References 295
34. Illustration Credits 309
35. Index 311