论文标题
中央四边形及其参考四边形之间的关系
Relationships between a Central Quadrilateral and its Reference Quadrilateral
论文作者
论文摘要
令P为凸四边形ABCD中的一个点。从P到四边形的顶点的线将四边形分为四个三角形。如果我们在每个三角形中的每个三角形中找到一个三角形中心，那么四个三角形中心将形成另一个四边形中心，称为中央四边形。对于各种形状的四边形以及1000个不同三角形中心的每个中心，我们将四边形的参考与中央四边形进行了比较。使用计算机，我们确定两个四边形是如何相关的。例如，我们测试以查看两个四边形是一致的，相似的，具有相同的区域或具有相同的周长。当p是与参考四边形相关的特殊点时，我们还会寻找这种关系，例如对角点，施泰纳点或poncelet点。
Let P be a point inside a convex quadrilateral ABCD. The lines from P to the vertices of the quadrilateral divide the quadrilateral into four triangles. If we locate a triangle center in each of these triangles, the four triangle centers form another quadrilateral called a central quadrilateral. For each of various shaped quadrilaterals, and each of 1000 different triangle centers, we compare the reference quadrilateral to the central quadrilateral. Using a computer, we determine how the two quadrilaterals are related. For example, we test to see if the two quadrilaterals are congruent, similar, have the same area, or have the same perimeter. We also look for such relationships when P is a special point associated with the reference quadrilateral, such as being the diagonal point, Steiner point, or Poncelet point.
