令SA_1…A_n表示以A_1,…,A_n为顶点的凸n边形面积.定义1一个凸n边形A_1A_2…A_n的内接中点n边形M_1M_2…M_n,为由这个凸n边形的n边中点M_i顺次连接构成的凸n边形.当n=5时,见图1.平面几何中最简单的知识告诉我们,对于任意三角形A_1A_2A_3和任意凸四边形A_1A_2A_3A_4,我们有面积比 Let SA_1 ... A_n denote the area of ​​convex n-vertices with A_1, ..., A_n as the vertices.Definition 1 The inner midpoint n-sided M_1M_2 ... M_n of a convex n-polygon A_1A_2 ... A_n is defined by When n = 5, see Figure 1. The simplest knowledge of plane geometry tells us that for any triangle A_1A_2A_3 and any convex quadrilateral A_1A_2A_3A_4, we have an area ratio