Feynman's lost lecture The motion of the planets around the Sun

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Two tacks, a string and a pencil An ellipse can be drawn using two tacks, a string and a pencil, whereby the string is attached to the tacks at F and F' and the pencil moved so that it keeps the string taut. Move point P below. The length of the string is represented by AB. So FP+F'P=AB. Clearly for an ellipse to be possible, the length of the string must be greater that the distance FF'. The ellipse can be made larger by increasing AB, and it's shape can be altered by changing the distance FF'.

The reflection property The ellipse has a geometrical property of fundamental importance to Feynman's lecture. If a light bulb were turned on at F and the inner surface of the ellipse reflected light like a mirror, then all the reflected rays would come back together at F'.