By David S. Richeson

Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gems to Buckminster Fuller's structures and gigantic all-carbon molecules. but Euler's formulation is so easy it may be defined to a baby. *Euler's Gem* tells the illuminating tale of this crucial mathematical idea.

From historic Greek geometry to today's state-of-the-art study, Euler's Gem celebrates the invention of Euler's liked polyhedron formulation and its far-reaching influence 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 ignored the formulation fullyyt; how Descartes virtually came upon it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means predicted through adapting it to be used with doughnut shapes, soft surfaces, and better dimensional shapes; and the way twentieth-century mathematicians found that each form has its personal Euler's formulation. utilizing great examples and diverse illustrations, Richeson provides the formula's many based and unforeseen functions, equivalent to displaying why there's consistently a few windless spot on the earth, the way to degree the acreage of a tree farm via counting timber, and the way many crayons are had to colour any map.

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