Area-Invariant Pedal-Like Curves Derived from the Ellipse

Dan Reznik; Ronaldo Garcia; Hellmuth Stachel

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arXiv · 2009.02581

Area-Invariant Pedal-Like Curves Derived from the Ellipse

Dan Reznik·Ronaldo Garcia·Hellmuth Stachel

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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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BibTeX RIS

Dan Reznik, Ronaldo Garcia, Hellmuth Stachel. 2020-09-16. Area-Invariant Pedal-Like Curves Derived from the Ellipse. https://arxiv.org/abs/2009.02581

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