Menelaus' and Ceva's theorems for translation triangles in Thurston geometries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908389550850048 |
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| author | Szirmai, Jenő |
| author_facet | Szirmai, Jenő |
| contents | After having investigated and defined the ``surface of a translation-like triangle" in each non-constant curvature Thurston geometry \cite{Cs-Sz25}, we generalize the famous Menelaus' and Ceva's theorems for translation triangles in the mentioned spaces.
The described method makes it possible to transfer further classical Euclidean theorems and notions to Thurston geometries with non-constant curvature. In our work we will use the projective models of Thurston geometries described by E. Molnár in \cite{M97}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Menelaus' and Ceva's theorems for translation triangles in Thurston geometries Szirmai, Jenő Geometric Topology Metric Geometry 53A20, 53A35, 52C35, 53B20 After having investigated and defined the ``surface of a translation-like triangle" in each non-constant curvature Thurston geometry \cite{Cs-Sz25}, we generalize the famous Menelaus' and Ceva's theorems for translation triangles in the mentioned spaces. The described method makes it possible to transfer further classical Euclidean theorems and notions to Thurston geometries with non-constant curvature. In our work we will use the projective models of Thurston geometries described by E. Molnár in \cite{M97}. |
| title | Menelaus' and Ceva's theorems for translation triangles in Thurston geometries |
| topic | Geometric Topology Metric Geometry 53A20, 53A35, 52C35, 53B20 |
| url | https://arxiv.org/abs/2506.01354 |