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Mechanical theorem proving in projective geometry

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Abstract

We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this prover and present a series of examples treated by the prover, includingPappus' andDesargues' theorems, thesixteen point theorem, Saam's theorem, thebundle condition, theuniqueness of a harmonic point andPascal's theorem.

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  1. FB Mathematik, Sekr. 6-1, Technische Universität Berlin, StraβBe des 17. Juni 135, D-10623, Berlin, Germany

    Jürgen Richter-Gebert

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Richter-Gebert, J. Mechanical theorem proving in projective geometry. Ann Math Artif Intell 13, 139–172 (1995). https://doi.org/10.1007/BF01531327

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