Given a polygon $P$ in the plane that can be translated, rotated and enlarged arbitrarily inside a unit square, the goal is to find a set of lines such that at least one of them always hits $P$ and the number of lines is minimized. We prove the solution is always a regular grid or a set of equidistant parallel lines, whose distance depends on $P$.
翻译:考虑到在飞机上可以任意翻译、旋转和扩大一个单位方形内的多边形美元,目标是找到一套线条,使其中至少有一条线条总是点击P美元,而线条数量也最小化。 我们证明解决方案总是一个常规网格或一套等距平行线条,其距离取决于P美元。