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A discrete isoperimetric problem

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

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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
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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