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Area-Invariant Pedal-Like Curves Derived from the Ellipse (2009.02581v3)
Published 5 Sep 2020 in math.MG, cs.GR, cs.RO, and math.DG
Abstract: 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.
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