Almost-tiling the plane by ellipses

Details Almost-tiling the plane by ellipses Almost-tiling the plane by ellipses

1998-04-07

arxiv.org/abs/math/9804040v1

Mathematics

Metric Geometry

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

Scientific paper

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.

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