Almost-tiling the plane by ellipses

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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.
11 pages, 11 figures. Dedicated to our friend Imre Bárány on the occasion of his 50th birthday

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Metric Geometry, 52C15

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http://salesiana.dossiersoluciones.com/handle/123456789/76805

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9804040
 http://arxiv.org/abs/math/9804040

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arXiv