Science/Engineering Euler's Gem: The Polyhedron Formula and the Birth of Topology (0691126771)

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David S. Richeson “Euler's Gem: The Polyhedron Formula and the Birth of Topology"

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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	Study Miyuki Kawamura - Polyhedron Origami for Beginners (Repost) Miyuki Kawamura - Polyhedron Origami for BeginnersJapan Publications Trading \| 2002 \| ISBN: 4889960856 \| Pages: 99 \| PDF \| 9.33 MBAn innovative approach to origami craft, polyhedron origami. introduces you into a new world of many-sided sol ...
	History/Military Letters of Euler to a German Princess: On Different Subjects in Physics and Philosophy: Leonard Euler Letters of Euler to a German Princess: On Different Subjects in Physics and Philosophy: Leonard Euler Thoemmes Continuum \| ISBN: 185506507X \| 1997-01-03 \| PDF (OCR) \| 1137 pages \| 19.0 Mb Leonhard Euler (1707-83) was one of the greatest ma ...
	Study Unit Polyhedron Origami Tomoko Fuse "Unit Polyhedron Origami"Japan Publications Trading \| English \| 2006-09-15 \| ISBN: 4889962050 \| 99 pages \| PDF \| 3,2 MBWith step-by-step diagrams, detailed instructions and over 70 photographs in vibrant full-color, internationa ...
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