Euler's Gem : : The Polyhedron Formula and the Birth of Topology / / David S. Richeson.
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...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English |
---|---|
VerfasserIn: | |
TeilnehmendeR: | |
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. |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
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