A staircase illumination theorem for orthogonal polygons (Q2381795)

The author elegantly proves the following theorem: ``Let \(S\) be a simply connected orthogonal polygon in the plane, and let \(T\) be a horizontal (or vertical) segment such that \(T'\cap S\) is connected for every translate \(T'\) of \(T\). If every two points of \(S\) see via staircase paths a common translate of \(T\), then there is a translate of \(T\) seen via staircase paths by every point of \(S\). That is, some translate of \(T\) is a staircase illuminator for \(S\). Clearly the number two is best possible.'' By means of an example it is shown that the requirement that \(T'\cap S\) be connected for translates \(T'\) of \(T\) is essential for this result to hold.