Nineteen Proofs of Euler's Formula: V-E+F=2
According to Malkevitch, this formula was discovered in around 1750 by Euler, and first proven by Legendre in 1794. Earlier, Descartes (around 1639) discovered a related polyhedral invariant (the total angular defect) but apparently did not notice the Euler formula itself. Hilton and Pederson provide more references as well as entertaining speculation on Euler's discovery of the formula. Confusingly, other equations such as ei pi = -1 and aphi(n) = 1 (mod n) also go by the name of "Euler's formula"
Euler's Formula
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