[math-fun] Folding a band saw blade

I took a look at https://www.youtube.com/watch?v=f-7x8X6I3RA because I needed to fold a kid's camping tent --- a task that poses similar differential-geometric challenges (but without the sharp teeth). The solution Paul Sellers advocates uses a table or other external object. Is there an easy-to-describe hands-only two-person solution? Also: Is there a write-up anywhere of the mathematics behind folding a band? I'm guessing that it's the kind of situation where you can get a (2n+1)-to-1 fold for any n. But I don't even see how the 3-to-1 fold works, nor do I see how one can rigorously prove that a 2-to-1 fold is impossible. Come to think of it, I don't even know how to state the problem as a mathematical one. Jim Propp