JOURNAL ARTICLE

On some relations between the perimeter, the area and the visual angle of a convex set.

  • Published In: Advances in Geometry, 2025, v. 25, n. 1. P. 105 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Bruna, J.; Cufí, J.; Reventós, A. 3 of 3

Abstract

We establish some relations between the perimeter, the area and the visual angle of a planar compact convex set. Our first result states that Crofton's formula is the unique universal formula relating the visual angle, the length and the area. After that we give a characterization of convex sets of constant width by means of the behavior of their isotopic sets at infinity. Also for this class of convex sets we prove that the existence of an isotopic circle is enough to ensure that the considered set is a disc. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Advances in Geometry. 2025/01, Vol. 25, Issue 1, p105
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:1615-715X
  • DOI:10.1515/advgeom-2024-0036
  • Accession Number:182413874
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