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Results in Mathematics

, Volume 52, Issue 3–4, pp 369–382 | Cite as

Pedal Curves Part I: Homogeneous Differential Equation

  • Angela Schwenk-SchellschmidtEmail author
Article
  • 73 Downloads

Abstract.

We study the class of plane curves with positive curvature κ and spherical parametrization s. t. that the curves and their derived curves like evolute, caustic, pedal and co-pedal curve, resp., have the same shape. We characterize these properties by a homogeneous linear differential equation of first order for the support function ρ and the radii of curvature κ -1 and we give a complete local classification of this class.

Keywords.

Euclidean plane curves curvature function support function pedal curve 

Mathematics Subject Classification (2000).

53A04 34A30 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.TFH BerlinBerlinGermany

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