Euler´s gem

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.