For 
,
 |  | ![a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)]](/images/equations/HypocycloidEvolute/Inline4.svg) |
(1)
|
 |  | ![a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)].](/images/equations/HypocycloidEvolute/Inline7.svg) |
(2)
|
If 
,
then
 |  | ![1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a](/images/equations/HypocycloidEvolute/Inline11.svg) |
(3)
|
 |  | ![1/(n-2)[(n-1)sinphi+sin[(n-1)phi]a.](/images/equations/HypocycloidEvolute/Inline14.svg) |
(4)
|
This is just the original hypocycloid scaled by the factor 
and rotated by 
of a turn.
Hypocycloid Evolute
See also
Hypocycloid, Hypocycloid Involute, InvoluteExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Hypocycloid Evolute." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HypocycloidEvolute.html