TOPICS
Search

Logarithmic Spiral Pedal Curve

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
LogarithmicSpiralPedal

The logarithmic spiral pedal curve is the pedal curve of a logarithmic spiral with respect to a pedal point at its pole. For a logarithmic spiral with parametric equations

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

the pedal curve has parametric equations

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)

For a in R, this is a similar logarithmic spiral, obtained from the original by uniform scaling by 1/sqrt(1+a^2) and a rotation through -tan^(-1)a about the pole. When a=0, both curves are the unit circle.

Explore with Wolfram|Alpha

Cite this as:

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

Subject classifications