A Dido problem as modernized by Fejes Tóth

Research output: Contribution to journalArticle

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 questions posed by Fejes Tóth.

Original languageEnglish (US)
Pages (from-to)227-238
Number of pages12
JournalDiscrete and Computational Geometry
Volume27
Issue number2
DOIs
StatePublished - Mar 2002

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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