If a coin rolls without slipping around another coin of the same or different size, how many times will it rotate while making one revolution?
The proof given is like this:
Cut the curve open at some point and uncoil it into a straight line segment. Rolling the circle along this segment it will rotate (length curve)/(length circle) times.
Keeping the circle attached to one end of the segment, we then recoil the segment back into thecurve, which contributes the final rotation.
I can understand the first part of the proof, but I couldn't understand the second part, any ideas? Also, I am also interested in different approaches for proving this one.