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 immense all-carbon molecules. but Euler's formulation is so uncomplicated it may be defined to a toddler. Euler's Gem tells the illuminating tale of this quintessential mathematical idea.
From old Greek geometry to today's state-of-the-art examine, Euler's Gem celebrates the invention of Euler's loved polyhedron formulation and its far-reaching impression 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 overlooked the formulation totally; how Descartes nearly stumbled on it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means expected through adapting it to be used with doughnut shapes, gentle surfaces, and better dimensional shapes; and the way twentieth-century mathematicians stumbled on that each form has its personal Euler's formulation. utilizing tremendous examples and various illustrations, Richeson provides the formula's many dependent and unforeseen functions, corresponding to displaying why there's consistently a few windless spot on the earth, 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.
Filled with a who's who of remarkable mathematicians who wondered, sophisticated, and contributed to a notable theorem's improvement, Euler's Gem will fascinate each arithmetic fanatic.