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 Comput Geom 29, 477–481 (2003). https://doi.org/10.1007/s00454-002-2835-z
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DOI: https://doi.org/10.1007/s00454-002-2835-z