Geodesic
Density of Optimal Packings of Three Ellipses in a Square
Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 201-209 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 52C15, 05B40, 51N20
Mots-clés : Packing, ellipse, density 
@article{JGG_2015_19_2_JGG_2015_19_2_a3,
     author = {P. Honvault },
     title = {Density of {Optimal} {Packings} of {Three} {Ellipses} in a {Square}},
     journal = {Journal for geometry and graphics},
     pages = {201--209},
     year = {2015},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a3/}
}
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P. Honvault . Density of Optimal Packings of Three Ellipses in a Square. Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 201-209. http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a3/