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Convex Polyhedra

  • Antonio Caminha Muniz Neto
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

We begin this chapter by defining and computing the area of a sphere and establishing a famous result of Girard on the area of a spherical triangle. Then, we present the important concept of convex polyhedron, which encompasses prisms and pyramids, and apply Girard’s theorem to prove the celebrated theorem of Euler, which asserts that the Euler characteristic of every convex polyhedron is equal to 2. The chapter finishes with using Euler’s theorem to obtain the classification of all regular polyhedra, and showing that all found possibilities do exist.

References

  1. 2.
    T. Apostol, Calculus, vol. 1 (Wiley, New York, 1967)Google Scholar
  2. 5.
    A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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