I'm sorry if this is too vague a question or is otherwise deemed poor quality.
The Background:
I've just seen an advert for the (new?) Coca Cola festive ribbon wrapper. Here's a picture:
A description of the ribbon making:
One takes a tab on the label of the bottle, pulls on it to strip away a band of the label until there's only a bit left attached to the rest, then one seems to pull on a different tab, and as one does so, the band that was peeled away ties itself into a lovely bow!
I'm curious . . .
The Question:
What is the mathematics behind how the ribbon wrapper works? Specifically, how does the ribbon tie itself in that way (with six such accurate "sub-bows")?
Thoughts:
I have no clue where to start in answering this, since, of course, it's a rather vague question. However, I suspect that someone here could be able to give some insight into what's going on.
There's some classical mechanics in there, at least; some knot theory, perhaps, although I'm aware that a knot in the mathematical sense is required to have its ends glued together seamlessly (so to speak); and maybe some origami.
My Background:
I did some classical mechanics during my A Levels but that's a long time ago now. I don't know anything about knot theory. As an undergraduate, I did a module in Galois theory and got a high grade; I don't know where I got this impression from but I think I recall that Galois theory is related to the mathematical study of origami, since compass & straight edge constructions are even more related to it and we study them using Galois theory; again, I haven't studied that in a while.
Please help :)
There is no deep mathematics involved in this construction; the bow is not even a knot. Try this for yourself:
Turn a pair of pants (trousers, for the British) inside out and put a belt in them. Pull the belt tight as far as it can go, so the pants are all bunched up next to the buckle end of the belt. Observe the resulting folds in the pants.
For greater fidelity, cut off all but the belt strip of the pants.