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
StatePublished - 2002

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Curve
Simple Polygon
Isoperimetric Inequality
Line segment
Intersect
Arrangement
Circle

ASJC Scopus subject areas

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

Cite this

A Dido problem as modernized by Fejes Tóth. / Siegel, Alan.

In: Discrete and Computational Geometry, Vol. 27, No. 2, 2002, p. 227-238.

Research output: Contribution to journalArticle

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