The evolute of the astroid is a hypocycloid evolute for 
. Surprisingly, it is another astroid
scaled by a factor 
and rotated 
of a turn. For an astroid with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  | ![1/2[3cost-cos(3t)]](/images/equations/AstroidEvolute/Inline12.svg) |
(3)
|
 |  | ![1/2[3sint+sin(3t)].](/images/equations/AstroidEvolute/Inline15.svg) |
(4)
|
Astroid Evolute
See also
Astroid, Astroid Involute, EvoluteExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Astroid Evolute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AstroidEvolute.html