A Property of Parallelograms Inscribed in Ellipses.

The article describes a property of ellipses which was observed by the physicist Jean-Marc Richard in connection with a problem from ballistics. The maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of the ellipse. The well-known geometric object to which the foregoing discussion relates is the orthoptic circle of Monge, who proved that the locus of points from which one sees an ellipse at right angles is a circle.