All tied in with the soup-plate trick, that wretched puzzle involving untangling the lines joining a ball to the corners of a surrounding cube, electron spin, Spin groups, and the simply-connected double cover of the 3-D Euclidean isometry group. None of is of the slightest use when wrestling with your band-saw blade, bicycle tyre or whatever; and I may not be of much assistance with said tent, the design of which is unfamiliar to me. The general approach with a stiffish band is (1) grasp horizontal loop at two diametrically opposite points A,B ; (2) rotate B through pi about axis AB , causing collision at C ; (3) simultaneously, allow B to rise and fold over, forming one-third size sub-loop; (4) allow A to rotate naturally through pi , causing collision at D ; (5) simultaneously, allow A to rise and fold over, forming one-third size sub-loop; (6) relax --- you (should) now have 3 unstressed sub-loops. WFL On 8/25/15, James Propp <jamespropp@gmail.com> wrote:
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.
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