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

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...

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Detalles Bibliográficos
Autor: Pacheco Castelao, José Miguel
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Repositorio:accedaCRIS portal de investigación de la Universidad de las Palmas de Gran Canaria
OAI Identifier:oai:accedacris.ulpgc.es:10553/5235
Acceso en línea:http://hdl.handle.net/10553/5235
Access Level:acceso abierto
Palabra clave:12 Matemáticas
Convex plane area
Isoperimetric inequality
Descripción
Sumario: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