Euler's Gem: The Polyhedron Formula and the Birth of Topology
Author: David S. Richeson
Publisher: Princeton University Press
In 1750, Euler observed that any polyhedron composed of V vertices, E edges and F faces satisfies the equation V-E+F=2. This tells how the Greeks missed the formula; how Descartes almost discovered it but fell short; how 19th-century mathematicians widened its scope by adapting it for use with doughnut shapes, smooth surfaces and higher dimensional shapes; and how 20th-century mathematicians found that every shape has its own Euler's formula.
Who is it for? Second- or final-year undergraduates with an interest in the history of mathematics.
Presentation: Entertaining, with fairly detailed maths in places: Richeson doesn't shy away from the maths.
Would you recommend it? Definitely. It's an excellent account of the historical context of today's topology and combinatorics.