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Arrangement of Central Points on the Faces of a Tetrahedron

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arxiv 2101.02592 v1 pith:FIWOVQZG submitted 2021-01-06 math.HO math.MG

Stanley Rabinowitz This is my paper
classification math.HOmath.MG
keywords tetrahedroncentersfacesfourlocatedpointsarrangementcentral
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We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of the tetrahedron. Using a computer, we determine when any of 16 conditions occur (such as the four centers being coplanar). A typical result is: The lines from each vertex of a circumscriptible tetrahedron to the Gergonne points of the opposite face are concurrent.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. More Relationships between a Central Quadrilateral and its Reference Quadrilateral

    math.GM 2025-06 conditional novelty 6.0 of 10

    For 28 quadrilateral shapes and 1000 triangle centers, the paper catalogs relationships such as area ratios, similarity, concurrence, and homothety between a quadrilateral and its central quadrilateral.

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