Covering a plane convex body by four homothetical copies with the smallest positive ratio (Q1057500)

This paper concerns the well-known property that every plane convex body C can be covered with four smaller positive homothetical copies. Namely, it is proved that C can be covered with four homothetical copies whose ratio is not greater than \(\sqrt{2}/2.\) The proof is based on the following lemma: It is possible to inscribe in C parallelograms P and Q such that the diagonals of P are parallel to the sides of Q and the diagonals of Q are parallel to the sides of P.