Gensane, Thierry; Honvault, Pascal Optimal packings of two ellipses in a square. (English) £ ¢ ¡
Résumé
For each real number E in ]0, 1], we describe the densest packing P E of two non-overlapping congruent ellipses of aspect ratio E in a square. E belongs to ]0, 1/2], [1/2, E 0 ] where E 0 = √ (6 √ 3 − 3)/11, and [E 0 , 1]. The technique of unavoidable sets-used by Friedman for proving the optimality of square packings-allows to prove the optimality of each packing P E .