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Guarding a Koch Fractal Art Gallery
Department of Mathematics and Statistics, Ohio Northern University, Ada, USA
Department of Mathematics and Statistics, Ohio Northern University, Ada, USA
- 1 Department of Mathematics and Statistics, Ohio Northern University, Ada, USA
- 2 Department of Mathematics and Statistics, Ohio Northern University, Ada, USA
Open Journal of Discrete Mathematics·Volume 02 (2012)·Pages 134–137·Published 31 October 2012·DOI10.4236/ojdm.2012.24026
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Abstract
This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such generalized art galleries are defined. We construct an art gallery in which one side is the Koch fractal and the other sides are three sides of a rectangle. The appropriate measure of coverage by guards is not the total number of guards but, rather, the guards-to-side ratio. We compute this ratio for the cases of shallow and deep versions of the Koch fractal art gallery.
KeywordsArt Gallery TheoremKoch FractalDifference Equation
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