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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 Curve

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References

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

Cite this as:

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

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