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arXiv · 2110.08877

On Menelaus' and Ceva's theorems in Nil geometry

Jenő Szirmai
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Abstract

In this paper we deal with $\NIL$ geometry, which is one of the homogeneous Thurston 3-geometries. We define the "surface of a geodesic triangle" using generalized Apollonius surfaces. Moreover, we show that the "lines" on the surface of a geodesic triangle can be defined by the famous Menelaus' condition and prove that Ceva's theorem for geodesic triangles is true in $\NIL$ space. In our work we will use the projective model of $\NIL$ geometry described by E. Moln\'ar in \cite{M97}.

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BibTeXRIS

Jenő Szirmai. 2021-10-17. On Menelaus' and Ceva's theorems in Nil geometry. https://arxiv.org/abs/2110.08877

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