Rolling on the outside
(follow up from the posts goo.gl/iYYd6b
If you can roll epicycloids/hypocycloids inside each other, then you can also roll them on the outside.
I was a bit puzzled to see that the cusps of a (n+1)-hypocycloid, rolling on the outside of a n-hypocycloid, seemed to trace out a n-epicycloid. But then I realised that it is probably obvious that they do. If you roll a n-epicycloid on the inside of a (n+1)-epicycloid, the cusps of the outer epicycloid lie on the inner epicycloid. So if you instead roll
epicycloids on the outside, the cusps of the (n+1)-epicycloid will glide along the inner n-epicycloid. Since the cusps of
(n+1)-epicycloids are the same points as the cusps of (n+1)-hypocycloids, it all makes sense.
The GeoGebra worksheet on GeoGebraTube:http://www.geogebratube.org/student/m104829