# Covering the Plane with Fat Ellipses without Non-Crossing Assumption

Discrete & Computational Geometry, Feb 2003

Abstract. Kershner proved in 1939 that the density of a covering of the plane by congruent circles is at least 2π/ $$\sqrt{27}$$ [3]. In 1950 L. Fejes Tóth [2] extended this result showing that the same density bound holds for coverings with congruent ellipses which do not cross''. In the present paper we prove that the non-crossing assumption is not necessary if the ellipses are sufficiently fat''.

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Heppes. Covering the Plane with Fat Ellipses without Non-Crossing Assumption, Discrete & Computational Geometry, 2003, 477-481, DOI: 10.1007/s00454-002-2835-z