Dynamic Billiards in Ellipse

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Dynamic billiards studies the motion of a small billiard ball (subject to no friction) on a pool table as it undergoes elastic collisions with the boundary (elliptical in this case). Alternatively, one can think of the path a light ray would take in the interior of a reflective boundary.

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This Demonstration lets you choose the position and direction on the boundary at which the ray is injected into the interior of the ellipse (the red arrow). The "aim" buttons aim the ray at either focus, drawn in blue (they can be hidden via the "foci" checkbox). A well-known property of the ellipse is that a ray through a focus will bounce off the wall once and then pass through the other focus. You can specify the number of reflections and the ellipse's semiaxes, and