A simple proof of the rectilinear art gallery theorem
Heikki Mannila, Derick Wood · International Journal of Computer Mathematics · 1985
The Rectilinear Art Gallery Theorem states that for a rectilinear art gallery with nwalls at most [n/4] guards are needed to keep the entire art gallery under observation. There have been two proofs of this result. The first proof depends on the quadrilateralization of the art gallery and is quite complicated. The second proof is direct, yet it depends on a graph-theoretic argument at one crucial point. Our proof, on the other hand, is direct, completely geometrical, and at the same time, simple.