# Ceva’s and Menelaus’ theorems in projective-metric spaces

@article{Kurusa2019CevasAM,
title={Ceva’s and Menelaus’ theorems in projective-metric spaces},
author={{\'A}rp{\'a}d Kurusa},
journal={Journal of Geometry},
year={2019},
volume={110},
pages={1-12}
}
• Á. Kurusa
• Published 12 July 2019
• Mathematics
• Journal of Geometry
AbstractWe prove that Ceva’s and Menelaus’ theorems are valid in a projective-metric space if and only if the space is any of the elliptic geometry, the hyperbolic geometry, or the Minkowski geometries.
3 Citations
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
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,
• J. Szirmai
• Mathematics
The Quarterly Journal of Mathematics
• 2021
In the present paper we study $\mathbf{S}^2\!\times\!\mathbf{R}$ and $\mathbf{H}^2\!\times\!\mathbf{R}$ geometries, which are homogeneous Thurston 3-geometries. We define and determine the

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