By David S. Richeson

ISBN-10: 0691154570

ISBN-13: 9780691154572

Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gem stones to Buckminster Fuller's constructions and big all-carbon molecules. but Euler's formulation is so easy it may be defined to a toddler. *Euler's Gem* tells the illuminating tale of this fundamental mathematical idea.

From historical Greek geometry to today's state-of-the-art learn, Euler's Gem celebrates the invention of Euler's cherished polyhedron formulation and its far-reaching impression on topology, the learn of shapes. In 1750, Euler saw 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 neglected the formulation totally; how Descartes nearly chanced on it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means predicted by way of adapting it to be used with doughnut shapes, delicate surfaces, and better dimensional shapes; and the way twentieth-century mathematicians came upon that each form has its personal Euler's formulation. utilizing fantastic examples and diverse illustrations, Richeson offers the formula's many based and unforeseen functions, corresponding to exhibiting why there's consistently a few windless spot in the world, the best way to degree the acreage of a tree farm by way of counting timber, and the way many crayons are had to colour any map.

packed with a who's who of magnificent mathematicians who puzzled, sophisticated, and contributed to a extraordinary theorem's improvement, *Euler's Gem* will fascinate each arithmetic enthusiast.

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**Example text**

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

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