Area-Invariant Pedal-Like Curves Derived from the Ellipse

September 05, 2020 · Declared Dead · 🏛 Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

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Authors Dan Reznik, Ronaldo Garcia, Hellmuth Stachel arXiv ID 2009.02581 Category math.MG Cross-listed cs.GR, cs.RO, math.DG Citations 4 Venue Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Last Checked 1 month ago
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 (Krümmungs-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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