Covering the plane by rotations of a lattice arrangement of disks

Details Covering the plane by rotations of a lattice arrangement of disks Covering the plane by rotations of a lattice arrangement of disks

2006-11-26

arxiv.org/abs/math/0611800v1

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

Suppose we put an $\epsilon$-disk around each lattice point in the plane, and then we rotate this object around the origin for a set $\Theta$ of angles. When do we cover the whole plane, except for a neighborhood of the origin? This is the problem we study in this paper. It is very easy to see that if $\Theta = [0,2\pi]$ then we do indeed cover. The problem becomes more interesting if we try to achieve covering with a small closed set $\Theta$.

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