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A forgotten little chapter on isoperimetric inequalities: On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

Jose M. Pacheco
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Abstract

Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle.

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Jose M. Pacheco. 2007-01-21. A forgotten little chapter on isoperimetric inequalities: On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter. https://arxiv.org/abs/math/0701589

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