Area-Invariant Pedal-Like Curves Derived from the Ellipse
Metric Geometry
2020-09-18 v3 Graphics
Robotics
Differential Geometry
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.
Keywords
Cite
@article{arxiv.2009.02581,
title = {Area-Invariant Pedal-Like Curves Derived from the Ellipse},
author = {Dan Reznik and Ronaldo Garcia and Hellmuth Stachel},
journal= {arXiv preprint arXiv:2009.02581},
year = {2020}
}
Comments
15 pages, 11 figures, 1 table