Gensane, Thierry; Honvault, Pascal Optimal packings of two ellipses in a square. (English) £ ¢ ¡ - Archive ouverte HAL Access content directly
Journal Articles Forum Geometricorum: A Journal on Classical Euclidean Geometry Year : 2014

Gensane, Thierry; Honvault, Pascal Optimal packings of two ellipses in a square. (English) £ ¢ ¡

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. 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 .
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hal-03620578 , version 1 (26-03-2022)

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  • HAL Id : hal-03620578 , version 1

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Pascal Honvault, Thierry Gensane. Gensane, Thierry; Honvault, Pascal Optimal packings of two ellipses in a square. (English) £ ¢ ¡. Forum Geometricorum: A Journal on Classical Euclidean Geometry, 2014. ⟨hal-03620578⟩
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