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.

中文翻译：

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将Ceva定理扩展到n-Simplices

摘要

涉及三角形的Ceva定理是后欧几里得平面几何的主要结果。三角形的三维概括是一个四面体，而它们的n维概括是一个n-单纯形。我们将Ceva定理扩展到n个单形，并以此说明在概括从平面几何到高维几何时可以做出的考虑和选择。