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- W3205348046 abstract "In this paper we deal with $NIL$ geometry, which is one of the homogeneous Thurston 3-geometries. We define the of a geodesic 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}." @default.
- W3205348046 created "2021-10-25" @default.
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- W3205348046 date "2021-10-17" @default.
- W3205348046 modified "2023-10-18" @default.
- W3205348046 title "On Menelaus' and Ceva's theorems in Nil geometry" @default.
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