Guarding a Koch Fractal Art Gallery

• 作者: Lauren Cassell William Roger Fuller
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: ART GALLERY THEOREM Koch FRACTAL DIFFERENCE Equation
• 年，卷（期）: 2012,（4）
• 页码范围: 134-137
• 页数: 4页
• 分类号: O1

摘要

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.