证明正交四球间15个垂心球及距离公式的算法——四维体积勾股定理的应用(公式(三))

The Proof of 15 Projective Spheres between Orthogonal Four Spheres and Algorithm of Distance Formula—Application of Pythagorean Theorem of Four Dimensional Volume (Formula (3))

摘要: 1球至4球正交球心构成的垂心四面体，存在4点、6线、4面、1体15个垂心球，这15个垂心球间的105个间距，除了可用2点坐标的距离公式计算外；还可以摆脱坐标直接利用垂心球间距公式计算。并且证明了同态重心与垂心间距为2球半径的平方差。

Abstract: A vertical tetrahedron consisting of four orthogonal sphere centers from one sphere to four spheres has 15 projective spheres of four points, six lines, four planes and one body. The 105 spacing between these 15 projective spheres can be calculated by the distance formula of two coordinates. It can also get rid of coordinates and calculate directly by using the formula of center of projective sphere spacing. It is also proved that the distance between the homomorphic center of gravity and the vertical center is the square variance of the radius of two spheres.