Guarding a Koch Fractal Art Gallery

Lauren Cassell; William Roger Fuller

doi:10.4236/ojdm.2012.24026

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Open Journal of Discrete Mathematics > Vol.2 No.4, October 2012

Guarding a Koch Fractal Art Gallery ()

Lauren Cassell, William Roger Fuller

Department of Mathematics and Statistics, Ohio Northern University, Ada, USA.

DOI: 10.4236/ojdm.2012.24026 PDF 5,049 Downloads 7,697 Views

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.

Keywords

Art Gallery Theorem; Koch Fractal; Difference Equation

Share and Cite:

L. Cassell and W. Fuller, "Guarding a Koch Fractal Art Gallery," Open Journal of Discrete Mathematics, Vol. 2 No. 4, 2012, pp. 134-137. doi: 10.4236/ojdm.2012.24026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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