论文标题
椭圆台球中三个周期的基因座：为什么这么多椭圆形？
Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
论文作者
论文摘要
三角形中心（例如，挖掘者，重中心等）是通过在侧长和/或角度上施加的函数和周期性应用的。考虑一下椭圆台球中的三个周期的第一家族，及其三角形中心的基因座。有些会扫过椭圆，而有些则将较高的代数曲线。我们提出了两种严格的方法，以证明给定中心的轨迹是椭圆的：一种基于计算机代数，另一种基于代数几何方法。我们还证明，如果三角中心函数在侧长上是合理的，则位点为代数
A triangle center such as the incenter, barycenter, etc., is specified by a function thrice- and cyclically applied on sidelengths and/or angles. Consider the 1d family of 3-periodics in the elliptic billiard, and the loci of its triangle centers. Some will sweep ellipses, and others higher-degree algebraic curves. We propose two rigorous methods to prove if the locus of a given center is an ellipse: one based on computer algebra, and another based on an algebro-geometric method. We also prove that if the triangle center function is rational on sidelengths, the locus is algebraic
