Datta, B
(1997)
*A discrete isoperimetric problem.*
In: Geometriae Dedicata, 64
(1).
pp. 55-68.

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## Abstract

We prove that the perimeter of any convex n-gons of diameter 1 is at most 2n sin(pi/2n). Equality is attained here if and only if n has an odd factor. In the latter case, there are (up to congruence) only finitely many extremal n-gons. In fact, the convex n-gons of diameter I and perimeter 2n sin(pi/2n) are in bijective correspondence with the solutions of a diophantine problem.

Item Type: | Journal Article |
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Publication: | Geometriae Dedicata |

Publisher: | Springer |

Additional Information: | Copyright of this article belongs to Springer. |

Keywords: | convex polygons;isoperimetric inequalities. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 01 Jun 2009 06:50 |

Last Modified: | 19 Sep 2010 05:00 |

URI: | http://eprints.iisc.ac.in/id/eprint/18236 |

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