arXiv:2009.02581
Area-Invariant Pedal-Like Curves Derived from the Ellipse
Area-Invariant Pedal-Like Curves Derived from the Ellipse
著者: Dan Reznik, Ronaldo Garcia, Hellmuth Stachel
分類: math.MG, cs.GR, cs.RO, math.DG
原文アブストラクト
We study six pedal-like curves associated with the ellipse which are area-invariant for pedal points lying on one of two shapes: (i) a circle concentric with the ellipse, or (ii) the ellipse boundary itself. Case (i) is a corollary to properties of the Curvature Centroid (Kr\"ummungs-Schwerpunkt) of a curve, proved by Steiner in 1825. For case (ii) we prove area invariance algebraically. Explicit expressions for all invariant areas are also provided.