Simple Proofs of the Generalized Oppenheim Inequalities
Received:May 04, 1993  
Key Words: metric sum   polygon   simplex   area   volume   radius.  
Fund Project:
Author NameAffiliation
Chen Ji Dept. of Appl. Math.
Ningbo Univ.
Ningbo 315211 
Wang Zhen Inst. of Math. & Phy. Sci.
Academia Sinica
Wuhan 430071 
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Abstract:
      Suppose A={A,…,An+1} consists of the venices of one simplex and B={B,…,Bn+1} consists another. A+B denotes a point set C={C,…, Cn+1} such that |Ci-Cj|2=|Ai-Aj|2+|Bi-Bj|2, i,j=1,…,n+1.Let V, V2, V and R, 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.
Citation:
DOI:10.3770/j.issn:1000-341X.1996.01.012
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