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} }
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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