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27 April 2024

» arxiv » math.MG/9804040

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Almost-tiling the plane by ellipses
Krystyna Kuperberg ; W{l}odzimierz Kuperberg ; Jiv{r}í Matouv{s}ek ; Pavel Valtr ;
Date:	7 Apr 1998
Subject:	Metric Geometry MSC-class: 52C15 \| math.MG
Abstract:	For any delta > 1 we construct a periodic and locally finite packing of the plane with ellipses whose delta-enlargement covers the whole plane. This answers a question of Imre Bárány. On the other hand, we show that if C is a packing in the plane with circular discs of radius at most 1, then its 1.00001-enlargement covers no square with side length 4.
Source:	arXiv, math.MG/9804040
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