An Extension of Ceva’s Theorem to n-Simplices

@article{Samet2021AnEO,
  title={An Extension of Ceva’s Theorem to n-Simplices},
  author={Dov Samet},
  journal={The American Mathematical Monthly},
  year={2021},
  volume={128},
  pages={435 - 445}
}
  • D. Samet
  • Published 28 May 2021
  • Mathematics
  • The American Mathematical Monthly
Abstract Ceva’s theorem, which concerns triangles, is a central result of post-Euclidean plane geometry. The three-dimensional generalization of a triangle is a tetrahedron, and the n-dimensional generalization of these is an n-simplex. We extend Ceva’s theorem to n-simplices and in doing so illustrate the considerations and choices that can be made in generalizing from plane geometry to high-dimensional geometries. 
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The paper is a continuation of an earlier article [5] concerning spatial versions of the well known theorems of Ceva and Menelaus. A necessary and sufficient condition for six points lying on edges…

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This article presents generalizations of the theorems of Ceva and Menelausfor n-dimensionalEuclideanspace.

A generalization of Ceva's theorem to higher dimensions

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