论文标题
椭圆台球中三角轨道的新特性
New Properties of Triangular Orbits in Elliptic Billiards
论文作者
论文摘要
作者在“椭圆台球能否仍然让我们惊讶的是我们的椭圆台球台球台上的一维轨道家族中的新不变式？” （2020），数学。 Intelligencer，42（1）：6--17，其中一些被推广到$ n> 3 $。那里提到的不变性包括半径和/或区域的比率，角余弦之和和一个特殊的固定圆。在这里，我们介绍那里省略的一些证据以及一些新的相关事实。
New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in "Can the Elliptic Billiard Still Surprise Us?" (2020), Math. Intelligencer, 42(1): 6--17, some of which were generalized to $N>3$. Invariants mentioned there included ratios of radii and/or areas, sum of angle cosines, and a special stationary circle. Here we present some of the proofs omitted there as well as a few new related facts.
