Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 2, pp. 309-320 (2007)
A staircase illumination theorem for orthogonal polygons
Marilyn BreenThe University of Oklahoma, Norman, Oklahoma 73019, U.S.A. e-mail: email@example.com
Abstract: Let $S$ be a simply connected orthogonal polygon in the plane, and let $T$ be a horizontal (or vertical) segment such that $T'\cap S$ is connected for every translate $T '$ of $T$. If every two points of $S$ see via staircase paths a common translate of $T$, then there is a translate of $T$ seen via staircase paths by every point of $S$. That is, some translate of $T$ is a staircase illuminator for $S$. Clearly the number two is best possible. The result fails without the requirement that each set $T ' \cap S$ be connected.
Keywords: Orthogonal polygons, staircase illumination
Classification (MSC2000): 52A30, 52A35
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Electronic version published on: 7 Sep 2007. This page was last modified: 28 Jun 2010.