一类涉及两个单形的三角不等式及其应用  

A Class of Triangle Inequalities Involving Two Simplices and Their Applications

作　　者：齐继兵[1] 杨世国[1] 

机构地区：[1]合肥师范学院数学系,合肥230061

出　　处：《数学的实践与认识》2008年第22期175-180,共6页Mathematics in Practice and Theory

基　　金：安徽省高等学校省级自然科学研究项目(KJ2008B54ZC);安徽省高校省级重点项目(2006KJ067A)

摘　　要：应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及两个n维单形的几何不等式问题,建立了涉及两个单形的一类三角不等式.作为其应用,获得了涉及两个单形及其内点的几何不等式,特别,获得了n维单形与其垂足单形的体积的一类关系式,改进了关于垂足单形体积的几类几何不等式.Using analytic method and theory of geometric inequality, the problem of geometric inequality involving two simplices in E^n is discussed, and a class of triangle inequalities involving two simplices and their interior points are established in this paper. As their applications, we can get a class of inequalities involving two simplices and their interior points. Specially, we get a class of inequalities on the volumes of simplex and its pedal simplex, some known inequalities on the volumes of simplex and its pedal simplex are improved.

关 键 词：垂足单形 内点 顶点角 空间角 不等式 

分 类 号：O178[理学—数学]