Ranunculoid

An epicycloid with cusps, named after the buttercup genus Ranunculus (Madachy 1979).

Its parametric equations are

			(1)
			(2)

Its arc length and area are given by

			(3)
			(4)

Its arc length function, curvature, and tangential angle are

			(5)
			(6)
			(7)

Explore with Wolfram|Alpha

More things to try:

ranunculoid
{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}
d/dx x^2 y^4, d/dy x^2 y^4

References

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, p. 223, 1979.Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 79-80, 1995.

Cite this as:

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

Ranunculoid

See also

Explore with Wolfram|Alpha

References

Cite this as:

Subject classifications