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Euler’s Polyhedron Formula in mizar

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Part of the Lecture Notes in Computer Science book series (LNTCS,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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References

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Alama, J. (2010). Euler’s Polyhedron Formula in mizar . In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_26

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)