Euler's Gem : : The Polyhedron Formula and the Birth of Topology /

Euler's Gem : : The Polyhedron Formula and the Birth of Topology / / David S. Richeson.

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How a simple equation reshaped mathematicsLeonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's theorem is so simple it can be explained to a child. From...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English
VerfasserIn:
Richeson, David S.,
TeilnehmendeR:
Richeson, David S.
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2019]
©2019
Year of Publication:2019
Language:English
Series:Princeton Science Library ; 82
Online Access:
Physical Description:1 online resource (336 p.) :; 221 b/w illus. 8 tables.
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Table of Contents:
  • Frontmatter
  • Contents
  • Preface to the Princeton Science Library Edition
  • Preface
  • Introduction
  • Chapter 1. Leonhard Euler and His Three "Great" Friends
  • Chapter 2. What Is a Polyhedron?
  • Chapter 3. The Five Perfect Bodies
  • Chapter 4. The Pythagorean Brotherhood and Plato's Atomic Theory
  • Chapter 5. Euclid and His Elements
  • Chapter 6. Kepler's Polyhedral Universe
  • Chapter 7. Euler's Gem
  • Chapter 8. Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes
  • Chapter 9. Scooped by Descartes?
  • Chapter 10. Legendre Gets It Right
  • Chapter 11. A Stroll through Königsberg
  • Chapter 12. Cauchy's Flattened Polyhedra
  • Chapter 13. Planar Graphs, Geoboards, and Brussels Sprouts
  • Chapter 14. It's a Colorful World
  • Chapter 15. New Problems and New Proofs
  • Chapter 16. Rubber Sheets, Hollow Doughnuts, and Crazy Bottles
  • Chapter 17. Are They the Same, or Are They Different?
  • Chapter 18. A Knotty Problem
  • Chapter 19. Combing the Hair on a Coconut
  • Chapter 20. When Topology Controls Geometry
  • Chapter 21. The Topology of Curvy Surfaces
  • Chapter 22. Navigating in n Dimensions
  • Chapter 23. Henri Poincaré and the Ascendance of Topology
  • Epilogue: The Million-Dollar Question
  • Acknowledgments
  • Appendix A: Build Your Own Polyhedra and Surfaces
  • Appendix B: Recommended Readings
  • Notes
  • References
  • Illustration Credits
  • Index

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