Circle Pedal Curve
CirclePedal
The pedal curve of a unit circle with parametric equation
x = cost
(1)
y = sint
(2)
with pedal point (x,y) is
x_p = cost-ycostsint+xsin^2t
(3)
y_p = 1/2[y+ycos(2t)+2sint-xsin(2t)].
(4)
The pedal curve with respect to the center is the circle itself (Gray 1997, pp. 119 and 124-135).
If the pedal point is taken on the circumference (and in particular at the point (1,0)), the pedal curve is the cardioid
x_p = cost+sin^2t
(5)
y_p = (1-cost)sint,
(6)
and otherwise is a limaçon.
See also
Circle, Pedal CurveExplore with Wolfram|Alpha
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References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.Referenced on Wolfram|Alpha
Circle Pedal CurveCite this as:
Weisstein, Eric W. "Circle Pedal Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CirclePedalCurve.html