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Euler's Gem : The Polyhedron Formula and the Birth of Topology /
Leonhard 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 formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, NJ :
Princeton University Press,
[2012]
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| Edición: | Course Book |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- Frontmatter
- Contents
- 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