Pedal Curves Part I: Homogeneous Differential Equation
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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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