【摘要】 设A是n维欧氏空间E~n中的一个非退化单形,它的切点单形为B,又以A的顶点和它的内切球心的连线与A的n+1个侧面的交点为顶点的单形设为D。若单形A,B,D的体积分别记为V(A),V(B),V(D),本文证明了V(B)≤V(D)≤(1/n~n)V(A)。更多还原

【Abstract】 Let A. （i=1, 2, …. n+1） be the vertex of a simplex ? in n-dimensionalEuclidean space Eⁿ, B_i （i=1, 2, …, n+1） be the tangent points at which theinscribed sphere of ? is tangent to the side faces of ?. Then the simplex ?with the tangent points as vertexes is called the tangent points simplex. Thestraight line A_iI intersects the surface A₁A₂…A_i-1A_i+1…A_n+1 of ? at the pointD_i Where I is the inner center of ?. Let ? be the simplex with the D_i （i=1,2,…, n+1） as its vertexes and V（?）, V（?）, V（?） be the volume of ?, ?,?, the following inequality is proved:V（?）≤V （?）≤（1/nⁿ）V（?）.更多还原