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. |