## Euler's Gem: The Polyhedron Formula and the Birth of TopologyLeonhard 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. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, |

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#### LibraryThing Review

User Review - ztutz - LibraryThingThis book is a very well written and easy to read introduction to why topology exists. The central theme of the book is Euler's polyhedron formula, which is so simple that anyone who knows how to ... Read full review

it gets 5 stars from me

### Contents

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 Platos Atomic Theory | 36 |

CHAPTER 5 Euclid and His Elements | 44 |

CHAPTER 6 Keplers Polyhedral Universe | 51 |

CHAPTER 7 Eulers Gem | 63 |

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 |

The MillionDollar Question | 265 |

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 Königsberg | 100 |

CHAPTER 12 Cauchys Flattened Polyhedra | 112 |

CHAPTER 13 Planar Graphs Geoboards and Brussels Sprouts | 119 |

CHAPTER 14 Its a Colorful World | 130 |

CHAPTER 15 New Problems and New Proofs | 145 |

CHAPTER 16 Rubber Sheets Hollow Doughnuts and Crazy Bottles | 156 |

Acknowledgments | 271 |

Build Your Own Polyhedra and Surfaces | 273 |

Recommended Readings | 283 |

Notes | 287 |

295 | |

Illustration Credits | 309 |

311 | |

### Other editions - View all

Euler's Gem: The Polyhedron Formula and the Birth of Topology David S. Richeson Limited preview - 2008 |

Euler's Gem: The Polyhedron Formula and the Birth of Topology David S. Richeson Limited preview - 2008 |