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.
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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
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