垂足单形的一个几何不等式及应用  

Geometric inequality for pedal simplex and its applications

作　　者：杨世国[1] 齐继兵[1] 

机构地区：[1]合肥师范学院数学系,合肥230061

出　　处：《沈阳工业大学学报》2007年第4期474-476,共3页Journal of Shenyang University of Technology

基　　金：安徽省高等学校自然科学基金重点资助项目(2006kj067A)

摘　　要：n维欧氏空间En中n维单形作为En中的一种基本凸体,它的几何性质非常具有一般性.关于n维单形的几何不等式研究,近期建立了许多重要几何不等式,然而,关于垂足单形几何不等式研究还是比较少,只建立了n维单形与其垂足单形体积的几何不等式.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n维单形的垂足单形的几何不等式问题,建立了n维单形与其垂足单形的外接球半径和内切球半径之间的一个几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.The n-dimension simplex is the basic convex body in the n-dimension Euclidean space. Its geometric nature is usually universal. Recently, many important geometric inequalities have been established for the geometric inequality of n-dimensional simplex. However, the study concerning the geometric inequality problem for the pedal simplex is very less. The inequalities for volumes of a simplex and its pedal simplex were investigated. Using analytic method and theory of geometric inequality, the problem of geometric inequality for the pedal simplex of a simplex in En was discussed. An inequality for the circumradius and inradius of a simplex and its pedal simplex was established. As the special case, some generalizations of the famous n-dimensional Euler inequality were obtained.

关 键 词：单形 外接球半径 内切球半径 垂足单形 不等式 

分 类 号：O184[理学—数学]