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Optimizing Area and Perimeter of Convex Sets for Fixed Circumradius and Inradius

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Abstract.

 In this paper two problems posed by Santaló are solved: we determine the planar convex sets which have maximum and minimum area or perimeter when the circumradius and the inradius are given, obtaining complete systems of inequalities for the cases (A, R, r) and (p, R, r).

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Authors and Affiliations

  1. Rènyi Institute of Mathematics, Budapest, Hungary, , , , , , HU

    Károly Böröczky Jr. & María A. Hernández Cifre

  2. Universidad Miguel Hernández, Elche, Spain, , , , , , ES

    G. Salinas

Authors
  1. Károly Böröczky Jr.
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  2. María A. Hernández Cifre
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  3. G. Salinas
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Additional information

This work is supported in part by Dirección General de Investigación (MCYT) BFM2001-2871, and by OTKA grants No 31984 and 30012

Received October 15, 2001; revised January 29, 2002

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Böröczky Jr., K., Hernández Cifre, M. & Salinas, G. Optimizing Area and Perimeter of Convex Sets for Fixed Circumradius and Inradius. Monatsh. Math. 138, 95–110 (2003). https://doi.org/10.1007/s00605-002-0486-z

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  • DOI: https://doi.org/10.1007/s00605-002-0486-z

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