### 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) |
---|---|

Pages (from-to) | 227-238 |

Number of pages | 12 |

Journal | Discrete and Computational Geometry |

Volume | 27 |

Issue number | 2 |

State | Published - 2002 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Discrete and Computational Geometry*,

*27*(2), 227-238.

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

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 27, no. 2, pp. 227-238.

}

TY - JOUR

T1 - A Dido problem as modernized by Fejes Tóth

AU - Siegel, Alan

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036003096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036003096&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036003096

VL - 27

SP - 227

EP - 238

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -