椭圆上台球的几何及其Poncelet网格
The Geometry of Billiards in Ellipses and their Poncelet Grids
摘要：
基于共焦中心二次曲线的性质，分析了椭圆中台球的几何性质。台球的延伸边在位于共焦椭圆和双曲线上的点处相遇。它们定义了相关的庞斯莱网格。如果台球是周期性的，那么它对椭圆上的初始顶点的任何选择都是封闭的。这就产生了一个连续变化的台球这是所谓的台球运动虽然它既不是一个欧几里德也不是一个射影运动。这种运动的扩展到相关的庞斯莱网格导致新的见解和不变量。
英文摘要：
The goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points which are located on confocal ellipses and hyperbolas. They define the associated Poncelet grid. If a billiard is periodic then it closes for any choice of the initial vertex on the ellipse. This gives rise to a continuous variation of billiards which is called billiard's motion though it is neither a Euclidean nor a projective motion. The extension of this motion to the associated Poncelet grid leads to new insights and invariants.
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