涉及单形内点的一个几何不等式及其应用  

A geometric inequality and its application for an interior point of simplex

作　　者：齐继兵[1] 杨世国[1] 

机构地区：[1]合肥师范学院数学系,安徽合肥230601

出　　处：《纯粹数学与应用数学》2008年第3期543-546,共4页Pure and Applied Mathematics

基　　金：安徽省高等学校省级自然科学研究项目(KJ2008854ZC);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E^n中涉及n维单形Ω_n与其内接单形Ω′_n以及Ω_n中内点之间的几何不等式问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径以及Ω_n中内点到各侧面距离之间的一个几何不等式,并给出了它的应用.Using analytic method and theory of geometric inequality, we study the problem of geometric inequalities concerning n-dimensional simplex Ωn and its inscribed simplex Ω′n and an interior point of Ωn in E^n.A geometric inequality for the circumradius of Ωn, and Ω′n and distance of interior point to side faces is estabished, which is an improvement of an important geometric inequality as application.

关 键 词：单形 外接球半径 内点 不等式 

分 类 号：O184[理学—数学]