By David S. Richeson

Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gem stones to Buckminster Fuller's structures and immense 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 quintessential mathematical idea.

From historic Greek geometry to modern state of the art learn, Euler's Gem celebrates the invention of Euler's cherished polyhedron formulation and its far-reaching influence on topology, the examine 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 completely; how Descartes virtually came across it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means anticipated by way of adapting it to be used with doughnut shapes, gentle surfaces, and better dimensional shapes; and the way twentieth-century mathematicians found that each form has its personal Euler's formulation. utilizing remarkable examples and diverse illustrations, Richeson offers the formula's many based and unforeseen functions, akin to displaying why there's regularly a few windless spot in the world, tips to degree the acreage of a tree farm via counting bushes, and the way many crayons are had to colour any map.

full of a who is who of tremendous mathematicians who puzzled, subtle, and contributed to a striking theorem's improvement, *Euler's Gem* will fascinate each arithmetic enthusiast.