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