重心是三角形三边中线的交点.重心到顶点的距离是它到对边中点的距离的两倍.重心和三角形三个顶点组成的三个三角形面积相等这些性质都是我们熟知的,但重心到三角形三个顶点距离之和是不是最小(等边三角形除外),则是一个需要研究的问题.在谈这个问题之前,先由一个古老的数学问题说起.原题是:在△ABC内找一点P,使其到三个顶点的 The center of gravity is the intersection of the triangle’s three centerlines. The distance between the center of gravity and the apex is twice that of the mid-point on the opposite side. The centers of the three triangles, the center of gravity and the triangle’s three vertices, are of equal area. To the triangle three vertices distance is not the minimum (except equilateral triangles), is a need to study the problem. Before talking about this question, first by an ancient mathematical problem. The original question is: within △ ABC Find a little P and make it to the three vertices