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Euler's Gem: The Polyhedron Formula and the Birth of Topology
Chapter 5. Euclid and His “Elements”
monograph
Publication date:
December 31 2012
Publisher:
Princeton University Press
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Trace Elements and Electrolytes
Author and book information
Book Chapter
Publication date:
December 31 2012
Pages
: 44-50
DOI:
10.1515/9781400838561.44
SO-VID:
43147df7-7789-4a64-8ce9-9622817fe535
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Book chapters
pp. i
Frontmatter
pp. ix
Preface
pp. vii
Contents
pp. 1
Introduction
pp. 10
Chapter 1. Leonhard Euler and His Three “Great” Friends
pp. 27
Chapter 2. What Is a Polyhedron?
pp. 31
Chapter 3. The Five Perfect Bodies
pp. 36
Chapter 4. The Pythagorean Brotherhood and Plato’s Atomic Theory
pp. 44
Chapter 5. Euclid and His “Elements”
pp. 51
Chapter 6. Kepler’s Polyhedral Universe
pp. 63
Chapter 7. Euler’s Gem
pp. 75
Chapter 8. Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes
pp. 81
Chapter 9. Scooped by Descartes?
pp. 87
Chapter 10. Legendre Gets It Right
pp. 100
Chapter 11. A Stroll through Königsberg
pp. 112
Chapter 12. Cauchy’s Flattened Polyhedra
pp. 119
Chapter 13. Planar Graphs, Geoboards, and Brussels Sprouts
pp. 130
Chapter 14. It’s a Colorful World
pp. 145
Chapter 15. New Problems and New Proofs
pp. 156
Chapter 16. Rubber Sheets, Hollow Doughnuts, and Crazy Bottles
pp. 173
Chapter 17. Are They the Same, or Are They Different?
pp. 186
Chapter 18. A Knotty Problem
pp. 202
Chapter 19. Combing the Hair on a Coconut
pp. 219
Chapter 20. When Topology Controls Geometry
pp. 231
Chapter 21. The Topology of Curvy Surfaces
pp. 241
Chapter 22. Navigating in n Dimensions
pp. 253
Chapter 23. Henri Poincaré and the Ascendance of Topology
pp. 265
Epilogue: The Million-Dollar Question
pp. 271
Acknowledgments
pp. 273
Appendix A. Build Your Own Polyhedra and Surfaces
pp. 283
Appendix B. Recommended Readings
pp. 287
Notes
pp. 295
References
pp. 309
Illustration Credits
pp. 311
Index
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