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

• Autores: José Miguel Pacheco Castelao
• Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 20, Nº. 1-2, 2008, págs. 113-118
• Idioma: inglés
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• Resumen

  • Often sorne interesting or simply curious points are left out when developing a theory. lt 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. lt is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle.