Teorema de Euler para poliedros convexos utilizando geometria esférica

Abstract

In this study, we investigated Euler's Theorem applied to convex polyhedra, establishing a relationship between vertices, edges and faces by means of a specific identity. Spherical Geometry was used in conjunction with the concepts and properties of Euclidean Geometry for convex polyhedra, which are fundamental for demonstrating the theorem. The main objective was to analyze the interrelationship between the elements of these polyhedra, adopting an integrated approach between Spherical Geometry and Euclidean Geometry. In order to fully understand Euler's Theorem for convex polyhedra, the relevant concepts and historical contexts were explored, with the aim of presenting characteristics that allow it to be generalized. Keywords: Euler's Theorem. Spherical Geometry. Convex polyhedra. Euclidean geometry