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

Euler's Gem: The Polyhedron Formula and the Birth of Topology
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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 out of 5 stars based on 0 reviews
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  • Euler's Gem: The Polyhedron Formula and the Birth of Topology
  • Written by author David S. Richeson
  • Published by Princeton University Press, 4/15/2012
  • 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
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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 Künigsberg 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

Acknowledgements 271

Appendix A Build Your Own Polyhedra and Surfaces 273

Appendix B Recommended Readings 283

Notes 287

References 295

Illustration Credits 309

Index 311


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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. <i>Euler's Gem</, Euler's Gem: The Polyhedron Formula and the Birth of Topology

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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. <i>Euler's Gem</, Euler's Gem: The Polyhedron Formula and the Birth of Topology

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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. <i>Euler's Gem</, Euler's Gem: The Polyhedron Formula and the Birth of Topology

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

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