四面体各面上中心点的排列
Arrangement of Central Points on the Faces of a Tetrahedron
摘要：
本文系统地研究了四面体上各种三角形中心（如正心或圆心）的性质。对于每六种类型的四面体，我们检查超过100个中心位于四面体的四面体。使用计算机，我们确定16个条件中的任何一个何时发生（例如四个中心共面）。一个典型的结果是：从一个外切四面体的每个顶点到相对面的Gergonne点的直线是共点的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
