Density of optimal packings of three ellipses in a square. - Archive ouverte HAL Access content directly
Journal Articles Journal for Geometry and Graphics Year : 2015

Density of optimal packings of three ellipses in a square.

Abstract

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.

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Dates and versions

hal-03620575 , version 1 (26-03-2022)

Identifiers

  • HAL Id : hal-03620575 , version 1

Cite

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⟩
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