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Ranunculoid

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Ranunculoid
RanunculoidFrames

An epicycloid with n=5 cusps, named after the buttercup genus Ranunculus (Madachy 1979).

Its parametric equations are

x=a[6cost-cos(6t)]
(1)
y=a[6sint-sin(6t)].
(2)

Its arc length and area are given by

s=48a
(3)
A=42pia^2.
(4)

Its arc length function, curvature, and tangential angle are

s(t)=(24)/5[1-sgn[sin(5/2t)]cos(5/2t)+2|_(5t)/(2pi)_|]
(5)
kappa(t)=7/(2r4a|sin(5/2t)|)
(6)
phi(t)=7/2t.
(7)

See also

Cardioid, Epicycloid, Nephroid

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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

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