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
Abstract
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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