Also called Chvátal's Art Gallery Theorem. If the walls of an art gallery are made up of straight Line Segments, then the entire gallery can always be supervised by watchmen placed in corners, where is the Floor Function. This theorem was proved by V. Chvátal in 1973. It is conjectured that an art gallery with walls and Holes requires watchmen.
See also Illumination Problem
References
Honsberger, R. ``Chvátal's Art Gallery Theorem.'' Ch. 11 in Mathematical Gems II.
Washington, DC: Math. Assoc. Amer., pp. 104-110, 1976.
O'Rourke, J. Art Gallery Theorems and Algorithms. New York: Oxford University Press, 1987.
Stewart, I. ``How Many Guards in the Gallery?'' Sci. Amer. 270, 118-120, May 1994.
Tucker, A. ``The Art Gallery Problem.'' Math Horizons, pp. 24-26, Spring 1994.
Wagon, S. ``The Art Gallery Theorem.'' §10.3 in Mathematica in Action. New York:
W. H. Freeman, pp. 333-345, 1991.