论文标题
三角形的芭蕾舞集中在椭圆台上
The Ballet of Triangle Centers on the Elliptic Billiard
论文作者
论文摘要
椭圆台球中三个周期家族的动态几何形状是神秘的。除了保护周边和伊拉迪乌斯（Inradius）与circumradius的比率外，它还有一个固定点。此外，其三角形中心扫除着令人着迷的基因座，包括椭圆，四分之一，圆圈和其他更复杂的曲线。在这里，我们探讨了与（i）3个周期性形状和（ii）某些三角形中心的运动学相关的新现象，这些运动学的某些三角形中心的运动学受到台球边界的约束，特别是某些非单调运动，某些人可以相对于3个周期。催眠是两个这样的非单调中心的联合运动，它们的许多停止和go类似于芭蕾舞。
The dynamic geometry of the family of 3-periodics in the Elliptic Billiard is mystifying. Besides conserving perimeter and the ratio of inradius-to-circumradius, it has a stationary point. Furthermore, its triangle centers sweep out mesmerizing loci including ellipses, quartics, circles, and a slew of other more complex curves. Here we explore a bevy of new phenomena relating to (i) the shape of 3-periodics and (ii) the kinematics of certain Triangle Centers constrained to the Billiard boundary, specifically the non-monotonic motion some can display with respect to 3-periodics. Hypnotizing is the joint motion of two such non-monotonic Centers, whose many stops-and-gos are akin to a Ballet.
