论文标题
才华横溢的反逆三角先生
The Talented Mr. Inversive Triangle in the Elliptic Billiard
论文作者
论文摘要
颠倒椭圆台球N-周期的顶点相对于以一个焦点为中心的圆圈产生了一个刻在帕斯卡（Pascal）的利马斯（Limaçon）中的新的“焦点与内向”家庭。以下是其令人惊讶的不变性：（i）周长，（ii）余弦之和（iii）从反转中心（焦点）到顶点的距离之和。我们在n = 3案例中证明了这些，表明这个家庭（a）具有固定的gergonne点，（b）是一个三个周期的家族，由第二个，刚性移动的椭圆机弯曲，（c）填料，Barycenter，Barycenter，Barycenter，Barycenter，OrtheCenter，OrtheCenter，Nine-Point Center，Ninine Point Center，以及许多其他的Triangle Circiangle circianders Cirgian courigners。
Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one focus yields a new "focus-inversive" family inscribed in Pascal's Limaçon. The following are some of its surprising invariants: (i) perimeter, (ii) sum of cosines, and (iii) sum of distances from inversion center (the focus) to vertices. We prove these for the N=3 case, showing that this family (a) has a stationary Gergonne point, (b) is a 3-periodic family of a second, rigidly moving elliptic billiard, and (c) the loci of incenter, barycenter, circumcenter, orthocenter, nine-point center, and a great many other triangle centers are circles.
