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arXiv · 2506.01354

Menelaus' and Ceva's theorems for translation triangles in Thurston geometries

Jenő Szirmai
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Abstract

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. Moln\'ar in \cite{M97}.

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Jenő Szirmai. 2025-06-02. Menelaus' and Ceva's theorems for translation triangles in Thurston geometries. https://arxiv.org/abs/2506.01354

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