folding steel bags

[eub]

Oxford origami engineers have published a paper giving a method of folding a paper bag down flat by "rigid origami" methods, i.e. bending it only at the creases. This invites the question of what's non-rigid about the usual method.

Playing with a paper bag, I'm not sure. It's certainly hard to fold it in a manner that is rigid, but I can't convince myself that it can't be done. The part that looks most suspicious to me is whether you have to twist the long vertical panels on the side, either that or bend the front and back. Can anyone see it? And describe it textually? :)

(Theorem 1 here says the state space of the rigidified traditional shopping bag is just the two isolated points "open" and "flat", but all the proofs are off in some full paper somewhere.)

Comments

[eub.livejournal.com]

Okay, the paper with proofs is here, but that does not look like it's going to be a gut-satisfying proof (I need another way to get to equation (2)) so I'm staring at shopping bags.

[zzyzx-xyzzy.livejournal.com]

I think if you operate the traditional grocery bag fold, the corners of the long vertical panels can't remain right angles. Or put another way, the boundary between the upper part of the bag and the lower, that's a rectangle in the open state, doesn't stay in the same plane through the fold, but would have to be if the upper portion folded rigidly.

[hattifattener]

I am resisting the urge to go play with a bag since I need to go get some sleep, but I think you are right.

I also think that the fact that a paper bag can't be folded "rigidly" probably contributes to its stability a bit.

[mh75.livejournal.com]

I have not been able to picture it being non rigid, either.

[boonedog.livejournal.com]

I have dyslexia when it comes to visual manipulation of shapes. No, I seriously do. So, in this context I am useless.