Euler's Gem: The Polyhedron Formula and the Birth of Topology (Google eBook)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. 
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Review: Euler's Gem: The Polyhedron Formula and the Birth of Topology
User Review  Matthewmartinmurray murray  GoodreadsThis was really fun to read at first but then goes heavily into topology and left me in the dust a little. I have a better understanding of some topological ideas but could have used a better ... Read full review
Review: Euler's Gem: The Polyhedron Formula and the Birth of Topology
User Review  Tox123  GoodreadsGreat book! Before I knew next to nothing on topology, now I know basic knot theory and a little graph theory. Read full review
Contents
1  
chapter1  10 
chapter2  27 
chapter3  31 
chapter4  36 
chapter5  44 
chapter6  51 
chapter7  63 
chapter17  173 
chapter18  186 
chapter19  202 
chapter20  219 
chapter21  231 
chapter22  241 
chapter23  253 
epilogue  265 
chapter8  75 
chapter9  81 
chapter10  87 
chapter11  100 
chapter12  112 
chapter13  119 
chapter14  130 
chapter15  145 
chapter16  156 
ack  271 
AppendixA  273 
AppendixB  283 
Notes  287 
295  
illcredits  309 
311  