论文标题
相似的相关性：椭圆台球中的三角形和三个周期性
Related by Similiarity: Poristic Triangles and 3-Periodics in the Elliptic Billiard
论文作者
论文摘要
威廉·查帕尔（William Chapple）于1746年发现，这是一组带有常见的cirt和cruckcircle的可变的三角形。从定义上讲，家庭具有恒定的inradius to-circumradius比率。有趣的是，这种不变性也适用于椭圆台球中三个周期的家族，尽管这里的inradius和prarradius是可变的，并且周长是恒定的。确实，我们显示一个家庭通过不同的相似性转换映射到另一个家庭。这意味着在一个家庭中观察到的任何无尺度的数量和不变性都必须持有另一个家庭。
Discovered by William Chapple in 1746, the Poristic family is a set of variable-perimeter triangles with common Incircle and Circumcircle. By definition, the family has constant Inradius-to-Circumradius ratio. Interestingly, this invariance also holds for the family of 3-periodics in the Elliptic Billiard, though here Inradius and Circumradius are variable and perimeters are constant. Indeed, we show one family is mapped onto the other via a varying similarity transform. This implies that any scale-free quantities and invariants observed in one family must hold on the other.
