Art Gallery Theorems and Algorithms

The Art Gallery Theorem is a result in computational geometry that addresses the problem of determining how many guards are needed to observe an art gallery (which can be represented as a polygon). The theorem states that for any simple polygon with \( n \) vertices, at most \( \left\lfloor \frac{n}{3} \right\rfloor \) guards are sufficient to cover the entire area of the polygon.