CEVA’S AND MENELAUS’ THEOREMS FOR TETRAHEDRA (II)

@article{Witczyski1996CEVASAM,
  title={CEVA’S AND MENELAUS’ THEOREMS FOR TETRAHEDRA (II)},
  author={Krzysztof Witczyński},
  journal={Demonstratio Mathematica},
  year={1996},
  volume={29},
  pages={233 - 236}
}
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 of a given te t rahedron to be ( oplanar is formulated. Similarly, a necessary and sufficient condition for six planes, each of them determined by an edge and the point on the opposi te edge, to have a common point is s ta ted. 
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Background Citations
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3 Citations

An Extension of Ceva’s Theorem to n-Simplices

Ceva’s theorem is extended to n-simplices and in doing so the considerations and choices that can be made in generalizing from plane geometry to high-dimensional geometries are illustrated.

Routh's theorem for simplices

It is shown in our earlier paper that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we first give another…

On the Steiner–Routh Theorem for Simplices

Another proof of the Steiner—Routh theorem for tetrahedra is given, where methods of elementary geometry are combined with the inclusion—exclusion principle, and this approach is generalized to (n — 1)-dimensional simplices.

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