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Logarithmic Spiral Involute

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LogarithmicSpiralInvolute
Logarithmic spiral involute animation

For a logarithmic spiral with parametric equations

x=e^(bt)cost
(1)
y=e^(bt)sint,
(2)

the involute is given by

x=(e^(bt)sint)/b
(3)
y=-(e^(bt)cost)/b,
(4)

which is another logarithmic spiral scaled by a factor of 1/b and rotated by an angle pi/2.

See also

Involute, Logarithmic Spiral

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Cite this as:

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

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