一组广义余弦定理探究

Study of A Seires of Generalized Cosine-Theorems

在引入边矢量及面矢量概念的基础上 ,以类比作为手段 ,对余弦定理进行由平面三角形到空间多边形乃至任意多面体的一系列推广 ,得出了形式对称一致的一组广义余弦定理 ,并给出了其简捷严谨的证明。

Basing on the introduction of brim-vector and face-vector, by means of analogy, the paper popularizes the cosine-theorem from flat-triangle to vacuum-polygon and arbitrary-polyhedron, concludes a series of generalized cosine-theorems which have symmetric and conformable form, and presents short and strict proof.