Euler's Gem The Polyhedron Formula and the Birth of Topology~tqw~ darksiderg

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  Euler's Gem The Polyhedron Formula and the Birth of Topology~tqw~ darksiderg
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• Added:
  07/01/2008
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  *******************************************************************************<br /> Euler's Gem: The Polyhedron Formula and the Birth of Topology <br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 18,929,762 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> <br /> <br /> Leonhard Euler's polyhedron formula describes the structure of many objects--<br /> from soccer balls and gemstones to Buckminster Fuller's buildings and giant all<br /> -carbon molecules. Yet Euler's formula is so simple it can be explained to a <br /> child. Euler's Gem tells the illuminating story of this indispensable <br /> mathematical idea.<br /> <br /> From ancient Greek geometry to today's cutting-edge research, Euler's Gem <br /> celebrates the discovery of Euler's beloved polyhedron formula and its far-<br /> reaching impact on topology, the study of shapes. In 1750, Euler observed that <br /> any polyhedron composed of V vertices, E edges, and F faces satisfies the <br /> equation V-E+F=2. David Richeson tells how the Greeks missed the formula <br /> entirely; how Descartes almost discovered it but fell short; how nineteenth-<br /> century mathematicians widened the formula's scope in ways that Euler never <br /> envisioned by adapting it for use with doughnut shapes, smooth surfaces, and <br /> higher dimensional shapes; and how twentieth-century mathematicians discovered <br /> that every shape has its own Euler's formula. Using wonderful examples and <br /> numerous illustrations, Richeson presents the formula's many elegant and <br /> unexpected applications, such as showing why there is always some windless spot <br /> on earth, how to measure the acreage of a tree farm by counting trees, and how <br /> many crayons are needed to color any map.<br /> <br /> Filled with a who's who of brilliant mathematicians who questioned, refined, and <br /> contributed to a remarkable theorem's development, Euler's Gem will fascinate <br /> every mathematics enthusiast.<br /> <br /> Table Of Contents<br /> <br /> Preface ix<br /> Introduction 1<br /> Chapter 1 Leonhard Euler and His Three Great Friends 10<br /> Chapter 2 What Is a Polyhedron? 27<br /> Chapter 3 The Five Perfect Bodies 31<br /> Chapter 4 The Pythagorean Brotherhood and Plato&rsquo;s<br /> Atomic Theory 36<br /> Chapter 5 Euclid and His Elements 44<br /> Chapter 6 Kepler&rsquo;s Polyhedral Universe 51<br /> Chapter 7 Euler&rsquo;s Gem 63<br /> Chapter 8 Platonic Solids, Golf Balls, Fullerenes, and<br /> Geodesic Domes 75<br /> Chapter 9 Scooped by Descartes? 81<br /> Chapter 10 Legendre Gets It Right 87<br /> Chapter 11 A Stroll through K&ouml;nigsberg 100<br /> Chapter 12 Cauchy&rsquo;s Flattened Polyhedra 112<br /> Chapter 13 Planar Graphs, Geoboards, and Brussels Sprouts 119<br /> Chapter 14 It&rsquo;s a Colorful World 130<br /> Chapter 15 New Problems and New Proofs 145<br /> Chapter 16 Rubber Sheets, Hollow Doughnuts, and<br /> Crazy Bottles 156<br /> Chapter 17 Are They the Same, or Are They Different? 173<br /> Chapter 18 A Knotty Problem 186<br /> Chapter 19 Combining the Hair on a Coconut 202<br /> Chapter 20 When Topology Controls Geometry 219<br /> Chapter 21 The Topology of Curvy Surfaces 231<br /> Chapter 22 Navigating in n Dimensions 241<br /> Chapter 23 Hermi Poincar&eacute; and the Ascendance of Topology 253<br /> Epilogue The Million-Dollar Question 265<br /> Acknowledgements 271<br /> Appendix A Build Your Own Polyhedra and Surfaces 273<br /> Appendix B Recommended Readings 283<br /> Notes 287<br /> References 295<br /> Index 309<br /> <br /> Product Details<br /> <br /> * ISBN: 0691126771<br /> * ISBN-13: 9780691126777<br /> * Format: Hardcover, 336pp<br /> * Publisher: Princeton University Press<br /> * Pub. Date: September 25, 2008<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader<br />
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