关于两个单形顶点的距离、侧面积及体积的不等式及其应用  

Inequlities for vertex distances and face areas and volumes of two simplexes with applications

作　　者：陈士龙[1] CHEN Shilong(Anhui Broadcasting Movie and Television College,Hefei 230011,China)

机构地区：[1]安徽广播影视职业技术学院

出　　处：《浙江大学学报（理学版）》2020年第1期81-85,共5页Journal of Zhejiang University（Science Edition）

基　　金：安徽省自然科学重点科研项目(KJ2015A351)

摘　　要：研究欧氏空间E n中两个单形顶点的距离、侧面积及体积之间的不等式问题。利用幂平均不等式、算术-几何不等式、Chebyshev不等式的性质以及τn=[M-m)^2/(n+1)M^2]^n+1/2n≥1,τ′n=[M^′-m′)^2/(n+1)M^′2]^n+1/2n≥1,得到涉及两个单形顶点的距离、侧面积和体积的一些几何不等式。所得不等式是对已有结果的指数推广和加强推广。In this paper,We discuss problem of geometric inequalities for vertex distance and face areas and volumes of two simplexes in the Euclidean space E n.By using the power mean inequality,inequality of arithmetic and geometric mean,the Chebyshev inequality andτn=[M-m)^2/(n+1)M^2]^n+1/2n≥1,τ′n=[M^′-m′)^2/(n+1)M^′2]^n+1/2n≥1,we obtain some geometric inequalities for vertex distance and face areas and volumes of two simplexes.These inequalities are the generalizations of the known results.

关 键 词：单形 体积 面积 顶点距离 不等式 

分 类 号：O184[理学—数学]