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Euler’s Polyhedron Formula in mizar

  • Jesse Alama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

Abstract

Euler’s polyhedron formula asserts for a polyhedron p that V − E + F = 2, where V, E, and F are, respectively, the numbers of vertices, edges, and faces of p. Motivated by I. Lakatos’s philosophy of mathematics as presented in his Proofs and Refutations, in which the history of Euler’s formula is used as a case study to illustrate Lakatos’s views, we formalized a proof of Euler’s formula formula in the mizar system. We describe some of the notable features of the proof and sketch an improved formalization in progress that takes a deeper mathematical perspective, using the basic results of algebraic topology, than the initial formalization did.

Keywords

Algebraic Topology Natural Deduction Proof Check Mizar Mathematical Library Mizar System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jesse Alama
    • 1
  1. 1.Center for Artificial Intelligence, Department of Computer Science, Faculty of Science and TechnologyNew University of LisbonPortugal

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