从四面体到N维单形的棱切球心、热尔岗点、奈格尔点及其坐标公式

Edge-Tangent’s Sphere Center, Gergonne Point, Nagel Point and Their Coordinate Formula from Tetrahedron to N-Simplex

四面体存在棱切球的充要条件是该四面体的三组对棱之和相等。对于存在棱切球的四面体,本文给出其棱切球心、热尔岗点、奈格尔点的坐标公式,并将这三者的坐标公式推广至存在棱切超球面的n维单形。

The sufficient and necessary condition for the tetrahedron to have an edge-tangent’s sphere is that the sum of the three groups of opposite sides is equal in the tetrahedron. For a tetrahedron with an edge-tangent’s sphere, the coordinate formula of the edge-tangent’s sphere center, Gergonne Point and Nagel Point is given in this paper, and the coordinate formulas of these three points are extended to n-simplex with an edge-tangent’s hypersphere.