The Art Gallery Problem by Kellen Hatheway '19, Monday, February 4

The Art Gallery Problem by Kellen Hatheway ’19, Monday, February 4, Mathematics Colloquium, 1 – 1:45 pm, Stetson Court Classroom 101.

Abstract:  How many guards are needed to view the entire area of an art gallery? Using computational geometry we can represent the art gallery as a simple polygon where the guards are represented by a point within the polygon. A set of points, S, is said to guard a polygon if for all points, p, there exists some q in S such that the line between p and q does not leave the polygon. Chvatal’s Theorem gives us an upper bound for the minimum number of guards for a polygon with n vertices. The proof for this theorem involves triangulation and graph coloring to reach an upper bound of ⌊n/3⌋.