1简介对于一个凸形,其内部任一点都能表示为凸形的某条弦的中点,但是对于一般的凸形,什么样的点能表示为凸形的某个内接中心对称凸多边形的中心?本文将对这个命题的推广进行讨论.以下为本文的主要结论.定理设Ω为平面上的凸形,定义T为Ω的所有内接中心对称凸多边形中心构成的集合,则图形T的面积S(T)满足 1 Introduction For a convex shape, any interior point can be expressed as the midpoint of a convex shape of a string, but for a general convex shape, what kind of point can be expressed as a convex one of the central symmetrical convex polygons This paper will discuss the promotion of this proposition.The following is the main conclusion of this paper: Theorem Let Ω be a convex on the plane and define a set of center of all inscribed centrosymmetric convex polygons whose T is Ω, the graph T The area S (T) is satisfied