MATC Mathematics Club
Madison Area Technical College
Professor Benjamin Collins, UW-Platteville
"Euler's Polyhedron Formula"
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Previous Lectures: (Fibonacci Trees: A Dream Come True),(A marvelously terrible algorithm from Leonhard Euler), (Mathematics to the Rescue: Centrality in Graphs)
Abstract: In 1750, Swiss mathematician Leonhard Euler stated his famous result that, "In any solid enclosed by planes, the sum of the number of solid angles the number of faces exceeds the number of edges by 2." In modern notation, we say that for a polyhedron where the number of faces is F, the number of edges is E, and the number of vertices is V,
F - E + V = 2
This formula is well known, and is used in classroom lessons from grade school to grad school. However, Euler's proof of the formula had a major flaw. I will present a proof that, while not perfect, comes as close as any proof for a general audience can expect to.
Ben Collins has been a member of UW-Platteville Mathematics Department since 2000. In 11 years at UWP, he has taught 17 different courses. Among his favorites are History of Math, Discrete Math, Calc II, and Elementary Statistics. An avid crossword puzzler, he knows the name of Bambi s aunt and the sequel to Typee.
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