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

Name: Euler's Gem The Polyhedron Formula and the Birth of Topology
Price: 9.25 USD
Availability: InStock
ISBN: 9780691154572

ISBN-10: 0691154570

ISBN-13: 9780691154572

Edition: 2008

Authors: David S. Richeson

List price: $17.99

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Description:

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 Gemtells the illuminating story of this indispensable mathematical idea.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 ofVvertices,Eedges, andFfaces satisfies the equationV-E+F=2. David Richeson tells how the Greeks missed the formula entirely;…

Book details

List price: $17.99
Copyright year: 2008
Publisher: Princeton University Press
Publication date: 4/20/2012
Binding: Paperback
Pages: 336
Size: 6.14" wide x 9.25" long x 0.71" tall
Weight: 1.210
Language: English

David S. Richeson is associate professor of mathematics at Dickinson College.



Preface


Introduction



Leonhard Euler and His Three "Great" Friends



What Is a Polyhedron?



The Five Perfect Bodies



The Pythagorean Brotherhood and Plato's Atomic Theory



Euclid and His Elements



Kepler's Polyhedral Universe



Euler's Gem



Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes



Scooped by Descartes?



Legendre Gets It Right



A Stroll through Kï¿½nigsberg



Cauchy's Flattened Polyhedra



Planar Graphs, Geoboards, and Brussels Sprouts



It's a Colorful World



New Problems and New Proofs



Rubber Sheets, Hollow Doughnuts, and Crazy Bottles



Are They the Same, or Axe They Different?



A Knotty Problem



Combing the Hair on a Coconut



When Topology Controls Geometry



The Topology of Curvy Surfaces



Navigating in n Dimensions



Henri Poincarï¿½ and the Ascendance of Topology


Epilogue: The Million-Dollar Question


Acknowledgments



Build Your Own Polyhedra and Surfaces



Recommended Readings


Notes


References


Illustration Credits


Index