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Triangle angle sums related to translation curves in $\SOL$ geometry

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arxiv 1703.06646 v1 pith:OHP4CD5A submitted 2017-03-20 math.MG

Jenő Szirmai This is my paper · ORCID
classification math.MG
keywords anglesumstranslationgeometriesgeometrytrianglesanalogousanalyse
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abstract

After having investigated the geodesic and translation triangles and their angle sums in $\NIL$ and $\SLR$ geometries we consider the analogous problem in $\SOL$ space that is one of the eight 3-dimensional Thurston geometries. We analyse the interior angle sums of translation triangles in $\SOL$ geometry and prove that it can be larger or equal than $\pi$. In our work we will use the projective model of $\SOL$ described by E. Moln\'ar in \cite{M97},

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

    math.GT 2025-06 reject novelty 5.0 of 10

    Menelaus' and Ceva's theorems are formulated and proved for translation triangles in Nil, Sol, and ~SL2R spaces using geometry-specific simple ratios.

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