Euler’s gem: the polyhedron formula and the birth of topology

David S. Richeson0691126771, 9780691126777

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 tells 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 of V vertices, E edges, and F faces satisfies the equation V – E + F =2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula. Using wonderful examples and numerous illustrations, Richeson presents the formula’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast.

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Table of contents :
FM.pdf……Page 2
ack.pdf……Page 286
Introduction.pdf……Page 16
chapter1.pdf……Page 25
chapter2.pdf……Page 42
chapter3.pdf……Page 46
chapter4.pdf……Page 51
chapter5.pdf……Page 59
chapter6.pdf……Page 66
chapter7.pdf……Page 78
chapter8.pdf……Page 90
chapter9.pdf……Page 96
chapter10.pdf……Page 102
chapter11.pdf……Page 115
chapter12.pdf……Page 127
chapter13.pdf……Page 134
chapter14.pdf……Page 145
chapter15.pdf……Page 160
chapter16.pdf……Page 171
chapter17.pdf……Page 188
chapter18.pdf……Page 201
chapter19.pdf……Page 217
chapter20.pdf……Page 234
chapter21.pdf……Page 246
chapter22.pdf……Page 256
chapter23.pdf……Page 268
epilogue.pdf……Page 280
AppendixA.pdf……Page 288
AppendixB.pdf……Page 298
endnote.pdf……Page 302
references.pdf……Page 310
index.pdf……Page 324