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

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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.

From ancient Greek geometry to today's cutting-edge r ...more

*Euler's Gem*tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge r ...more

## Get A Copy

Hardcover, 317 pages

Published
September 28th 2008
by Princeton University Press
(first published 2008)

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## Community Reviews

Showing 1-30

V-E+F=2, also known as Euler's Formula. This formula originally described a relationship between the faces, edges, and vertices of the 5 platonic Solids, but actually has a deeper significance as an equation connecting the vast subtopics of topology, including graph theory, knot theory, the 4-co ...more

If this book is excellent, why four rather than five stars? It's because of the medium. This book was brought to my ...more

Dec 17, 2008
Daniela
is currently reading it

I am more or less in the middle of this book and I'm loving it. It explains, with simple words, the relevance of the polyhedron formula; filled up with history and proofs. Thumbs up!

"Sure!" I said, and handed him this book. "Here's algebraic topology!"

"Great," he said. "Any others?"

I looked at my shelf, saw that the answer was no, and realized in that moment how unusual Richeson's achievement is. This is an engaging, readable, historical tour, covering a large swath of interesting math, pitched at an appr ...more

The title of the book is derived from the formula V - E + F = 2 that holds for any convex polyhedron. V is the number of vertices, E the number of edges and F the number of faces. First demonstrated by Euler, the proof of this result is surprisingly simple. As is the case with most such formulas and their proofs, there is at least one near miss in the history of mathematics. Descartes was close; in retrospect it is somewh ...more

*Euler's Gem*is more or less what popular mathematics should be: it ...more

*Learn Gujrati in 30 Days*, and this was something like that. My kid was too young to realize that it was hard to understand and just had a lot of fun. We read about a chapter a night for weeks and weeks. At the very end of the book was a ...more

These are Poincaré's words author quotes at the end of the book. And he very well manages to show the nature's beauty in his book. More of biography/history of science than actual Mathematical technicalities so if you are ...more

A quote I liked...

“Scientists and engineers have used computers to solve countless problems, but mathematicians have not. Computers are good at making speedy calculations, but not at the kind of precise and subtle arguments that are required in mathematical proof. Like philosophy and art, mathematics has always been a human endeavor, one that cannot be automated.” David S. Richeson, Euler’s Gem

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General comment | 1 | 5 | Dec 14, 2013 10:19AM |

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David Richeson is a professor of mathematics at Dickinson College and the editor of

*Math Horizons*, the undergraduate magazine of the Mathematical Association of America. He received his undergraduate degree from Hamilton College and his masters and PhD from Northwestern University. He lives with his wife and two children in Carlisle, Pennsylvania.No trivia or quizzes yet. Add some now »

“In his life of seventy-six years, Euler created enough mathematics to fill seventy-four substantial volumes, the most total pages of any mathematician. By the time all of his work had been published (and new material continued to appear for seventy-nine years after his death) it amounted to a staggering 866 items, including articles and books on the most cutting-edge topics, elementary textbooks, books for the nonscientist, and technical manuals. These figures do not account for the projected fifteen volumes of correspondence and notebooks that are still being compiled.”
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