The physicist \ J.-M. Richard observed, in connection with a problem from ballistics, that the maximal perimeter of a parallelogram inscribed in a given ellipse can be attained by a parallelogram with one vertex at any prescribed point of the ellipse, and he gave a direct computational proof in [Eur. J. Phys. 25, No. 6, 835--844 (2004; Zbl 1162.70320)]. \ In the paper under review, the authors give two simple proofs, one geometric and the other algebraic, together with a slight generalization, and they describe connection with billiards.
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Connes et al. (2007) studied this question.