Cardioid Negative Pedal Curve
CardioidNegativePedalCurveCircle
For the cardioid given parametrically as
x = a(1+cost)cost
(1)
y = a(1+cost)sint,
(2)
the negative pedal curve with respect to the pedal point (x_0,y_0)=(0,0) is the circle
x_n = a(1+cost)
(3)
y_n = asint.
(4)
CardioidNegativePedalCurveCissoid
For the pedal point (2a,0), the negative pedal curve is a cissoid of Diocles with equation
x_n = -2/3acos(1/2t)^2
(5)
y_n = 2/3asin^2(1/2t)tan(1/2t).
(6)
See also
Cardioid, Cardioid Pedal Curve, Negative Pedal CurveExplore with Wolfram|Alpha
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References
Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 157, 1967.Referenced on Wolfram|Alpha
Cardioid Negative Pedal CurveCite this as:
Weisstein, Eric W. "Cardioid Negative Pedal Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CardioidNegativePedalCurve.html