
Journal for Geometry and Graphics 19 (2015), No. 2, 201209 Copyright Heldermann Verlag 2015 Density of Optimal Packings of Three Ellipses in a Square Pascal Honvault LMPA J. Liouville, Université du Littoral, Centre Universitaire de la MiVoix, 50 rue F. Buisson  CS80699, 62228 Calais, France honvault@lmpa.univlittoral.fr We prove that the most dense packing of three nonoverlapping congruent ellipses of aspect ratio E, 0 < E < 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 nonoverlapping congruent ellipses. Keywords: Packing, ellipse, density. MSC: 52C15; 05B40, 51N20 [ Fulltextpdf (462 KB)] 