论文标题
多边形中心的对称性与巧合和共线性之间的关系和平面中多集的中心
The relation between symmetries and coincidence and collinearity of polygon centers and centers of multisets of points in the plane
论文作者
论文摘要
有几个显着的点，定义为平面中的多边形和多个点，称为中心（例如质心）。为了使他们的研究成为可能，在这两种情况下都存在正式定义中心概念。在本文中，研究了多边形的对称性与平面中的多个点之间的关系以及其中心的巧合和截然性。首先，给出了问题的确切陈述。然后，证明，给定平面中的多边形或多个点的多数，当且仅当它属于其对称组固定的点集时，平面中的给定点才是该对象的中心。
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a formal definition for the concept of center in both cases. In this paper, the relation between symmetries of polygons and multisets of points in the plane and the coincidence and collinearity of their centers is studied. First, a precise statement for the problem is given. Then, it is proved that, given a polygon or a multiset of points in the plane, a given point in the plane is a center for this object if and only if it belongs to the set of points fixed by its group of symmetries.
