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Aequationes mathematicae

, Volume 89, Issue 6, pp 1433–1447 | Cite as

On evolutoids of planar convex curves II

  • V. A. Aguilar-Arteaga
  • R. Ayala-Figueroa
  • I. González-García
  • J. Jerónimo-Castro
Article
  • 141 Downloads

Abstract

In this paper we continue the study of evolutoids of convex curves. We proved that if a curve is homothetic to one of its evolutoids then it is a circle. This result is analogous, for the case of evolutoids, to the planar case of the famous homothetic floating body problem which states that if a floating body is homothetic to the body itself then it is an ellipsoid. Among other things, we proved that a curve and any of its evolutoids have the same Steiner point. Moreover, some relations between evolutoids and constant angle caustics are also given, for instance, that if for a given angle the left and right evolutoids describe the same curve then the curve possesses a constant angle caustic.

Mathematics Subject Classification

53A04 

Keywords

Convex evolutoid Convex floating body Illumination body Constant angle caustic 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • V. A. Aguilar-Arteaga
    • 1
  • R. Ayala-Figueroa
    • 1
  • I. González-García
    • 1
  • J. Jerónimo-Castro
    • 1
  1. 1.Universidad Autónoma de Querétaro, QuerétaroQuerétaroMexico

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