The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy'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.

中文翻译：

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使用柯西方法的欧拉公式的基本证明

使用柯西的方法证明欧拉的著名公式是许多争议的对象。本文的目的是证明Cauchy方法不仅适用于凸多面体，而且适用于凸多面体，还适用于诸如圆环，投影平面，Klein瓶和捏紧的圆环之类的表面。