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Logarithmic Spiral Catacaustic

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LogarithmicSpiralCatacaustic

The catacaustic of a logarithmic spiral, where the origin is taken as the radiant point, is another logarithmic spiral. For an original spiral with parametric equations

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

the catacaustic with radiant point at the origin is

x_c=(2be^(bt))/(1+b^2)(bcost-sint)
(3)
y_c=(2be^(bt))/(1+b^2)(bcost+sint).
(4)

See also

Catacaustic, Logarithmic Spiral

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References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 207, 1972.

Referenced on Wolfram|Alpha

Logarithmic Spiral Catacaustic

Cite this as:

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

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