Art Gallery Theorem
Also called Chvátal's Art Gallery Theorem. If the walls of an art gallery aremade 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 byV. Chvátal in 1973. It is conjectured that an art gallery with walls and 
Holes requires
watchmen.
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.
- Real Quadratic Field
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