A ray is reflected multiple times inside an ellipse. The black dots are the two foci of the ellipse. Studying billiards in simple geometric domains is a fascinating area of research. Much nontrivial mathematics results from investigating billiards, despite its simplicity. Closed periodic paths are especially relevant in Gutzwiller's trace formula (and its extensions); they comprise a beautiful piece of physics that links classical and quantum mechanics.

vertical half-axis length — length of the vertical half-axis of the ellipse, measured in units of the length of the horizontal half-axis number of reflections — number of reflections to carry out starting position — starting position of the ray starting angle — starting angle of the ray, measured against the normal erected at the starting point