Ranunculoid
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) = [画像:(24)/5[1-sgn[sin(5/2t)]cos(5/2t)+2|_(5t)/(2pi)_|]]
![画像:(24)/5[1-sgn[sin(5/2t)]cos(5/2t)+2|_(5t)/(2pi)_|]](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Ranunculoid/Inline16.svg){kind=link}
(5)
kappa(t) = [画像:7/(2r4a|sin(5/2t)|)]
(6)
phi(t) = 7/2t.
(7)
See also
Cardioid, Epicycloid, NephroidExplore with Wolfram|Alpha
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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.Referenced on Wolfram|Alpha
RanunculoidCite this as:
Weisstein, Eric W. "Ranunculoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Ranunculoid.html