Almost-tiling the plane by ellipses
Metric Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/9804040,
title = {Almost-tiling the plane by ellipses},
author = {Krystyna Kuperberg and Włodzimierz Kuperberg and Jiří Matoušek and Pavel Valtr},
journal= {arXiv preprint arXiv:math/9804040},
year = {2007}
}
Comments
11 pages, 11 figures. Dedicated to our friend Imre B\'ar\'any on the occasion of his 50th birthday