Manifold-based Proving Methods in Projective Geometry

Michael Martin Katzenberger; Jürgen Richter-Gebert

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arXiv · 2601.17446

Manifold-based Proving Methods in Projective Geometry

Michael Martin Katzenberger·Jürgen Richter-Gebert

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Abstract

This article compares different proving methods for projective incidence theorems. In particular, a technique using quadrilateral tilings recently introduced by Sergey Fomin and Pavlo Pylyavskyy is shown to be at most as strong as proofs using bi-quadratic final polynomials and thus, also proofs using Ceva-Menelaus-tilings. Furthermore, we demonstrate the equivalence between quadrilateral-tiling-proofs and proofs using exclusively Menelaus configurations. We exemplify the transition between the proofs in several examples in 2D and in 3D.

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Michael Martin Katzenberger, Jürgen Richter-Gebert. 2026-01-24. Manifold-based Proving Methods in Projective Geometry. https://arxiv.org/abs/2601.17446

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