 The study and generalization of this equation, specially by Cauchy and Lhuillier, is at the origin of topology.Euler characteristic, which may be generalized to any topological space as the alternating sum of the Betti numbers, naturally arises from homology.In particular, it is equal to 2 − 2"g" for a closed oriented surface with genus "g" and to 2 − "k" for a non-orientable surface with k crosscaps.