In general, the pedal curve of the cardioid
is a slightly complicated function.
The pedal curve of the cardioid with respect to the center of its conchoidal circle is the limaçon
trisectrix (Ferréol).
For the special pedal point of the cardioid cusp, the pedal curve of the cardioid
is
which is Cayley's sextic (Gray 1997, pp. 119-120).
See also
Cardioid,
Cardioid Negative Pedal Curve,
Cayley's Sextic,
Limaçon
Trisectrix,
Pedal Curve
Explore with Wolfram|Alpha
References
Ferréol, R. "Limaçon Trisectrix." https://mathcurve.com/courbes2d.gb/limacon/limacontrisecteur.shtml.Gray,
A. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, 1997.Referenced on Wolfram|Alpha
Cardioid Pedal Curve
Cite this as:
Weisstein, Eric W. "Cardioid Pedal Curve."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CardioidPedalCurve.html
Subject classifications