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|
|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|
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