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Thierry Gensane and Pascal Honvault, Optimal packings of two ellipses in a square,
Forum Geometricorum, 14 (2014) 371--380.
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Abstract. 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. We find three different patterns as E belongs to ]0,1/2], [1/2,E_0] where E_{0}=sqrt((6sqrt(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.

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