Astroid Evolute
AstroidEvolute
The evolute of the astroid is a hypocycloid evolute for n=4. Surprisingly, it is another astroid scaled by a factor n/(n-2)=4/2=2 and rotated 1/(2·4)=1/8 of a turn. For an astroid with parametric equations
x = cos^3t
(1)
y = sin^3t,
(2)
x_e = 1/2[3cost-cos(3t)]
(3)
y_e = 1/2[3sint+sin(3t)].
(4)
See also
Astroid, Astroid Involute, EvoluteExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Astroid Evolute." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AstroidEvolute.html