垂心四面体4态的正弦余弦定律及其换元算法——四维体积勾股定理的应用(公式六)

The Law of Sines and Cosines of the Orthocentric Tetrahedron with 4-State and Its Substitution Algorithm—Application of Pythagorean Theorem of Four Dimensional Volume (Formula 6)

摘要: 正交4球心组成的垂心四面体，仅用四球半径和垂心球间距公式。证明了3组正弦定理、5组余弦定理；各2组2面角的正弦定理、余弦定理；且证明了同构于球面三角学的正弦定律和余弦定律。垂心四面体4态换元算法，使得计算更为直观和简便。

Abstract: The Orthocentric Tetrahedron composed of orthogonal quadrature spherical center, using only quadrature spherical radius and spacing formula of Projective Sphere. Three sets of sine theorems and five sets of cosine theorems are proved. Sine theorem and cosine theorem of Angle between 2 planes; The law of sine and law of cosine isomorphic to spherical trigonometry are proved. The 4-state substitution algorithm of The Orthocentric Tetrahedron makes the calculation more intui-tive and simple.