  In the art gallery problem, we are given a closed polygon $P$, with rational
coordinates and an integer $k$. We are asked whether it is possible to find a
set (of guards) $G$ of size $k$ such that any point $p\in P$ is seen by a point
in $G$. We say two points $p$, $q$ see each other if the line segment $pq$ is
contained inside $P$. It was shown by Abrahamsen, Adamaszek, and Miltzow that
there is a polygon that can be guarded with three guards, but requires four
guards if the guards are required to have rational coordinates. In other words,
an optimal solution of size three might need to be irrational. We show that an
optimal solution of size two might need to be irrational. Note that it is
well-known that any polygon that can be guarded with one guard has an optimal
guard placement with rational coordinates. Hence, our work closes the gap on
when irrational guards are possible to occur.
