TOPICS
Search

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

Cardioid, Catacaustic

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Cardioid Catacaustic

Cite this as:

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

Subject classifications