Euler's Gem The Polyhedron Formula and the Birth of Topology 

Author:
 Richeson, David S. 
ISBN:  9780691154572 
Publication Date:  Mar 2012 
Publisher:  Princeton University Press

Book Format:  Paperback 
List Price:  AUD $44.99 
Book Description:

Leonhard Euler's polyhedron formula describes the structure of many objectsfrom soccer balls and gemstones to Buckminster Fuller's buildings and giant allcarbon 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 cuttingedge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its...
More Description
Leonhard Euler's polyhedron formula describes the structure of many objectsfrom soccer balls and gemstones to Buckminster Fuller's buildings and giant allcarbon 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 cuttingedge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its farreaching 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 VE+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenthcentury 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 twentiethcentury 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.