垂心四面体的勾股4态15个外接球半径、外心坐标及距离的算法——四维体积勾股定理的应用(公式九)

Calculation of Radius, Circumcenter Coordinates and Distance of 15 Circumscribed Spheres of Pythagorean 4-State in an Orthocentric Tetrahedron—Application of Pythagorean Theorem of Four-Dimensional Volume (Formula 9)

摘要: 用正交4球半径的4元数，证明：垂心四面体的勾股4态的15个外接球半径同构公式、外心坐标同构公式；及其用外接球半径计算外心距离公式；以及12组棱角、6组面角，它们的互补对角的正弦余弦的代数值公式。

Abstract: By using the quaternions of orthogonal 4-sphere radius, it is proved that there are 15 isomorphic formulas of circumscribed sphere radius and circumcenter coordinate isomorphism of the Py-thagorean 4-state of the orthocentric tetrahedron, and the formula of calculating the distance of the circumcenter by using the radius of circumscribed sphere, as well as 12 sets of angles, 6 sets of face angles, their complementary diagonal sine and cosine of the numerical formula.