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Logarithmic Spiral Pedal Curve

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LogarithmicSpiralPedal

The pedal curve of a logarithmic spiral with parametric equation

f=e^(at)cost
(1)
g=e^(at)sint
(2)

for a pedal point at the pole is an identical logarithmic spiral

x=((asint+cost)e^(at))/(1+a^2)
(3)
y=((sint-acost)e^(at))/(1+a^2),
(4)

so

r=sqrt(x^2+y^2)=(e^(at))/(sqrt(1+a^2)).
(5)

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Cite this as:

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

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