Optimal Packings of Two Ellipses in a Square

  title={Optimal Packings of Two Ellipses in a Square},
  author={Thierry Gensane and Pascal Honvault},
For each real number E in ]0, 1], we describe the densest packing PE of two non-overlapping congruent ellipses of aspect ratio E in a square. We find three different patterns as E belongs to ]0, 1/2], [1/2, E0] where E0 = √ (6 √ 3− 3)/11, and [E0, 1]. The technique of unavoidable sets – used by Friedman for proving the optimality of square packings – allows to prove the optimality of each packing PE . 

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Packing and covering with circles

  • H. Melissen
  • Ph.D. Thesis, Utrecht University
  • 1997
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