A discrete isoperimetric problem

Datta, Basudeb (1997) A discrete isoperimetric problem Geometriae Dedicata, 64 (1). pp. 55-68. ISSN 0046-5755

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Official URL: http://www.springerlink.com/content/w1133x82778747...

Related URL: http://dx.doi.org/10.1023/A:1004997002327


We prove that the perimeter of any convex n-gons of diameter 1 is at most n2nsin (π/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 1 and perimeter n2n sin (π/2n) are in bijective correspondence with the solutions of a diophantine problem.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Convex Polygons; Isoperimetric Inequalities
ID Code:22355
Deposited On:23 Nov 2010 12:59
Last Modified:23 Nov 2010 12:59

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