An elementary proof of Euler's formula using Cauchy's method

摘要

The use of Cauchy & rsquo;s method to prove Euler & rsquo;s well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy & rsquo;s method applies for convex polyhedra and not only for them , but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus.(c) 2020 Elsevier B.V. All rights reserved.