Density of optimal packings of three ellipses in a square.

Pascal Honvault (1, 2)

1 ULCO - Université du Littoral Côte d'Opale
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We prove that the most dense packing of three non-overlapping congruent ellipses of aspect ratio E ∈]0, 1] in a square is obtained for E = 1/3, with density equal to π/4. This result was already known for two ellipses (for E = 1/2), but is no longer true for an arbitrary number of non-overlapping congruent ellipses.

Mots clés: packing; ellipse; density

Domaines: Mathématiques [math]

Pascal Honvault. Density of optimal packings of three ellipses in a square.. Journal for Geometry and Graphics, 2015, 19 (2), pp.201-209. ⟨hal-03620575⟩