Logarithmic Spiral Catacaustic
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 = [画像:(2be^(bt))/(1+b^2)(bcost-sint)]
(3)
y_c = [画像:(2be^(bt))/(1+b^2)(bcost+sint).]
(4)
See also
Catacaustic, Logarithmic SpiralExplore with Wolfram|Alpha
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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 CatacausticCite this as:
Weisstein, Eric W. "Logarithmic Spiral Catacaustic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogarithmicSpiralCatacaustic.html