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.
Product Identifiers
Publisher
Princeton University Press
ISBN-13
9780691154572
eBay Product ID (ePID)
113837904
Product Key Features
Number of Pages
336 Pages
Language
English
Publication Name
Euler's Gem: the Polyhedron Formula and the Birth of Topology
Publication Year
2012
Subject
Mathematics
Type
Textbook
Author
David S. Richeson
Format
Paperback
Dimensions
Item Height
235 mm
Item Weight
539 g
Item Width
152 mm
Additional Product Features
Country/Region of Manufacture
United States
Title_Author
David S. Richeson
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