Princeton University Press
Euler's Gem: The Polyhedron Formula and the Birth of Topology
Key Metrics
- David S Richeson
- Princeton University Press
- Paperback
- 9780691154572
- 9.1 X 6 X 0.9 inches
- 1.19 pounds
- Mathematics > History & Philosophy
- English
Secure TransactionBook Description
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.
Author Bio
I am a professor of mathematics and the John J. Curley ’60 and Ann Conser Curley ’63 Faculty Chair in the Liberal Arts at Dickinson College.
I graduated from Hamilton College in 1993 with a degree in mathematics, and I received a Ph.D. in mathematics from Northwestern University in 1998. I came to Dickinson after a postdoctoral position at Michigan State University.
I am passionate about many areas of mathematics, but my research focuses on dynamical systems, topology, the history of mathematics, and recreational mathematics. I am the author of Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (2019) and Euler’s Gem: The Polyhedron Formula and the Birth of Topology (2008), both of which were published by Princeton University Press. I was the editor of Math Horizons, the undergraduate magazine of the Mathematical Association of America, from 2014 to 2019. I enjoy chatting about mathematics on my blog (Division by Zero) and on Twitter (@divbyzero).
My Erdös number is four in at least three ways (Erdös ? Andrzej Schinzel ? Michal Misiurewicz ? John Franks ? Me; Erdös ? Svante Janson ? Steve Fisher ? John Franks ? Me; Erdös ? Branko Grünbaum ? Jaume Llibre ? John Franks ? Me).
Source: divisbyzero.com
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