• Corpus ID: 239016129

On Menelaus' and Ceva's theorems in Nil geometry

@inproceedings{Szirmai2021OnMA,
  title={On Menelaus' and Ceva's theorems in Nil geometry},
  author={JenHo Szirmai},
  year={2021}
}
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. Molnár in [6]. 
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Classical Notions and Problems in Thurston Geometries
Of the Thurston geometries, those with constant curvature geometries (Euclidean E3, hyperbolic H3, spherical S3) have been extensively studied, but the other five geometries, H2×R, S2×R, Nil, S̃L2R,…

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