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Cardioid Pedal Curve

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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).

CardioidPedal

For the special pedal point of the cardioid cusp, the pedal curve of the cardioid

x=a(1+cost)cost
(1)
y=a(1+cost)sint,
(2)

is

x_p=2cos^4(1/2t)(2cost-1)
(3)
y_p=2cos^3(1/2t)sin(3/2t),
(4)

which is Cayley's sextic (Gray 1997, pp. 119-120).

See also

Cardioid, Cardioid Negative Pedal Curve, Cayley's Sextic, Limaçon Trisectrix, Pedal Curve

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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.

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Cardioid Pedal Curve

Cite this as:

Weisstein, Eric W. "Cardioid Pedal Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CardioidPedalCurve.html

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