Covering the plane by rotations of a lattice arrangement of disks

Abstract

Suppose we put an $ε$-disk around each lattice point in the plane, and then we rotate this object around the origin for a set $Θ$ 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 $Θ= [0,2π]$ then we do indeed cover. The problem becomes more interesting if we try to achieve covering with a small closed set $Θ$.

8 pages