### 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 language | English (US) |
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Pages (from-to) | 227-238 |

Number of pages | 12 |

Journal | Discrete and Computational Geometry |

Volume | 27 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2002 |

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### ASJC Scopus subject areas

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