volume 27, issue 2, P227-238 2002
DOI: 10.1007/s00454-001-0063-6
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Abstract: Let a finite number of line segments be located in the plane. Let C be a circle that surrounds the segments. Define the region enclosed by these segments to be those points that cannot be connected to C by a continuous curve, unless the curve intersects some segment. We show that the area of the enclosed region is maximal precisely when the arrangement of segments defines a simple polygon that satisfies a fundamental isoperimetric inequality, and thereby answer the most basic of the modern day Dido-type quest…

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