关于四面体对棱棱长比和二面角正弦比的定理

The Theorem of Opposite Edge Length Ratio and Dihedral Angle Sine Ratio in the Tetrahedron

摘要: 本文给出了四面体的三组对棱棱长之比以及三组对棱所夹二面角正弦比的定理，推导出四面体的对棱棱长、对棱所夹的二面角正弦值与该四面体各侧面面积、外接圆半径之间的关系。

Abstract: In this paper, we give the theorem of the ratio of the three pairs of opposite edges length and the sine ratio of three pairs of opposite edges between their dihedral angles in the tetrahedron, the relationship between the opposite edges length, the sine of the opposite edges between their dihedral angles of a tetrahedron and the area of each side and the circumradius is deduced in the tetrahedron.