摘要
设 E^n 中 n 维单形(?)={A_1,A_2,…,A_(n+1)}的顶点集为{A_1,A_2,…,A_(n+1)},有向体积为 V(?),以{A_1,A_(i-1),A_(i+1),…A_n)为顶点集的 n-1维单形(?)称为(?)的“侧面”(下文中(?)所在的 n-1维超平面也记为(?)),“侧面”(?)的 n-1维体积记为(?).自 E^n 中任意一点 M 向超平面(?),(?),…,(?)作垂线,垂足分别为 H_1,H_2,…,H_(n+1),则称顶点集是{H_1,H_2,…,H_(n+1)}的单形(?)_M 为 M 关于(?)的垂足单形,其 n
In this paper,we propose the vertex coordinate formula and two valume formulas on sim-plex with feet of perpendicular as vertexes and a trigonometric inequality on the higher di-mensional space vertex-angle.By means of these conclusions,we completely solve the conjec-ture put forth by Su Huaming (Shuxue Tongbao,5(1985),43—46).Besides,we have gener-alized and improved the main results of some previous papers.
出处
《系统科学与数学》
CSCD
北大核心
1992年第4期371-375,共5页
Journal of Systems Science and Mathematical Sciences
