Journal for Geometry and Graphics 19 (2015), No. 2, 201--209
Copyright Heldermann Verlag 2015
Density of Optimal Packings of Three Ellipses in a Square
LMPA J. Liouville, Université du Littoral, Centre Universitaire de la Mi-Voix, 50 rue F. Buisson - CS80699, 62228 Calais, France
We prove that the most dense packing of three non-overlapping 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 non-overlapping congruent ellipses.
Keywords: Packing, ellipse, density.
MSC: 52C15; 05B40, 51N20
[ Fulltext-pdf (462 KB)] for subscribers only.