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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.17446 |
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| _version_ | 1866918303707955200 |
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| author | Katzenberger, Michael Martin Richter-Gebert, Jürgen |
| author_facet | Katzenberger, Michael Martin Richter-Gebert, Jürgen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17446 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manifold-based Proving Methods in Projective Geometry Katzenberger, Michael Martin Richter-Gebert, Jürgen Combinatorics Computational Geometry 05B35, 51A20, 51A45 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. |
| title | Manifold-based Proving Methods in Projective Geometry |
| topic | Combinatorics Computational Geometry 05B35, 51A20, 51A45 |
| url | https://arxiv.org/abs/2601.17446 |