通过圆盘的格子排列的旋转覆盖平面
Covering the plane by rotations of a lattice arrangement of disks
摘要：
假设我们在平面中的每个晶格点周围放置一个$ε$ -圆盘，然后我们围绕原点旋转这个物体一组$Θ$角度。我们什么时候覆盖整个平面，除了原点的邻域？这就是本文研究的问题。很容易看出，如果$Θ= [0,2π]$，那么我们确实覆盖。如果我们试图用一个小的闭集$Θ$来实现覆盖，这个问题就变得更有趣了。
英文摘要：
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 $Θ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
