Archiv der Mathematik

, Volume 79, Issue 2, pp 147–157 | Cite as

Optimizing the perimeter and the area of convex sets with fixed diameter and circumradius

  • M. A. Hernández Cifre


We determine the planar convex sets which have the minimum area or perimeter when the diameter and the circumradius are prescribed. We use then these results to obtain the complete systems of inequalities for the cases (p, d, R) and (A, d, R).


Complete System Minimum Area Planar Convex Fixed Diameter 
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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • M. A. Hernández Cifre
    • 1
  1. 1.Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, Facultad de Matemáticas, 30100-Murcia, Spain,¶ e-mail:

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