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Almost-tiling the plane by ellipses

By Krystyna Kuperberg, Włodzimierz Kuperberg, Jiří Matoušek and Pavel Valtr

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 B\'ar\'any. 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.Comment: 11 pages, 11 figures. Dedicated to our friend Imre B\'ar\'any on the occasion of his 50th birthda

Topics: Mathematics - Metric Geometry, 52C15
Year: 1998
OAI identifier: oai:arXiv.org:math/9804040

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