Cardioid Catacaustic
The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x.
CardioidCatacaustic
For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for the cardioid given parametrically as
x = a(1+cost)cost
(1)
y = a(1+cost)sint
(2)
reduces to the nephroid
x_c = 1/4[2+3cost-cos(3t)]
(3)
y_c = sin^3t,
(4)
illustrated above.
See also
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References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 207, 1972.Referenced on Wolfram|Alpha
Cardioid CatacausticCite this as:
Weisstein, Eric W. "Cardioid Catacaustic." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CardioidCatacaustic.html