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Euler's Gem : the Polyhedron Formula and the Birth of Topology Preview this item
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Euler's Gem : the Polyhedron Formula and the Birth of Topology

Author: David S Richeson
Publisher: Princeton, NJ, USA : Princeton University Press, 2012.
Edition/Format:   Print book : EnglishView all editions and formats
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Genre/Form: Ressources Internet
History
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David S Richeson
ISBN: 9780691126777 0691126771 9780691154572 0691154570
OCLC Number: 1003609433
Awards: Winner of Mathematical Association of America's Euler Book Prize 2010
Short-listed for Choice Magazine Outstanding Reference/Academic Book Award 2009
Description: 1 ressource en ligne (332 pages)
Contents: 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 Konigsberg 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 Poincare 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
Responsibility: Richeson, David S.

Abstract:

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  Read more...

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Winner of the 2010 Euler Book Prize, Mathematical Association of America One of Choice's Outstanding Academic Titles for 2009 "The author has achieved a remarkable feat, introducing a naive reader to Read more...

 
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