Journal for Geometry and Graphics 25 (2021), No. 2, 227--230
Copyright Heldermann Verlag 2021
A Note on Some Generalizations of Monge's Theorem
University of Science and Technology, Bydgoszcz, Poland
We generalize Monge's theorem for n+1 pairwise homothetic sets (in particular convex bodies) in En in place of three disks in E2. We also present a version for homotheties for pairs of vertices of a non degenerate simplex in En. It includes a reverse of Monge's theorem. Moreover, we give an analogon of Monge's theorem for the n-dimensional sphere and hyperboloid model of the hyperbolic space.
Keywords: Monge's theorem, Menelaus' theorem, Euclidean space, sphere, hyperbolic space.
MSC: 52A20; 52A21, 52A55.
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