The involute of the astroid is a hypocycloid involute for 
. Surprisingly, it is another astroid
scaled by a factor 
and rotated 
of a turn. For an astroid with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  | ![1/8[3cost-cos(3t)]](/images/equations/AstroidInvolute/Inline12.svg) |
(3)
|
 |  | ![1/8[3sint+sin(3t)].](/images/equations/AstroidInvolute/Inline15.svg) |
(4)
|
Astroid Involute
See also
Astroid, Astroid Evolute, InvoluteExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Astroid Involute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AstroidInvolute.html