| 陈计,王振.Oppenheim不等式推广的简单证明[J].数学研究及应用,1996,16(1):62~64 |
| Oppenheim不等式推广的简单证明 |
| Simple Proofs of the Generalized Oppenheim Inequalities |
| 投稿时间：1993-05-04 |
| DOI：10.3770/j.issn:1000-341X.1996.01.012 |
| 中文关键词: |
| 英文关键词:metric sum polygon simplex area volume radius. |
| 基金项目: |
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| 中文摘要: |
| 设Ｅｕｃｌｉｄ空间ｎ＋１元点集Ａ，Ｂ及其度量和Ｃ所构成的单形的体积、外接球半径分别为Ｖ１，Ｖ2，Ｖ和Ｒ１，Ｒ2，Ｒ．本文给出不等式V2/n≥V12/n+V22/n,R2≤R12+R22一种简单的证法．该 |
| 英文摘要: |
| Suppose A={A１,…,An+１} consists of the venices of one simplex and B={B１,…,Bn+１} consists another. A+B denotes a point set C={C１,…, Cn+１} such that |Ci-Cj|2=|Ai-Aj|2+|Bi-Bj|2, i,j=1,…,n+1.Let V１, V2, V and R１, R2, R be the volumes and radio of the cirumscribed spheres of A, B, C respectively. Simple proofs are given on the followins inequalities due to Yang and Zhang:V2/n≥V12/n+V22/n,R2≤R12+R22 A related inequality for polygons is also proved. |
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