Why does paper fold so well?

Oh no! woe is me, they don't highlight my absolutely, ridiculously favourite fact/curiosity about a sheet of smooth paper:

If you fold it clean, the crease is a straight line. In fact I don't know of any other good way of obtaining a straight edge from scratch quickly, meaning without transporting one existing straight edge to another (*).

I remember spending a lot of enamored time coming up with different geometrical proofs of this fact. Perhaps the only time I have come close to jumping out of the proverbial bath tub.

The underlying reason is that paper does not stretch (**) (but, paradoxically, it does bend fine. It's a paradox because bending needs stretching).

I have to restrain myself from grabbing strangers off the streets to ask -- how cool is that.

Three other demonstrations that never fail to nerd-snipe me like this are Dirac's belt trick, that straight woven cloth rips usually at 90 degrees, and the working of a teeny tiny metacircular interpreter.

(*) Rope stretching is a close competitor, but the tension needs to be really really high and it is difficult to run a pencil along it to mark a straight line, lest you distort the st. line.

(**) of course, it does, but a tiny amount.

Coming back to straight line folds, this property holds beyond just Euclidean space, it holds for Riemannian geometry and probably for any continuous metric space.

It has a lot of air gaps within its fibers.

We know that Solids CANNOT be compressed. So what's actually being folded is the air gaps.

Which is why you can't easily fold a piece of tungsten. It has less air gaps.

Nice old video about this: https://www.youtube.com/watch?v=EKEavnS10HI

Unless I'm missing a transcript somewhere, this is missing an [audio] tag.

And why does it sink. Its basically squished wood!

This is exactly the sort of hard-hitting journalism that makes me proud to pay my TV licence.

A lovely little podcast on paper physics for origami.

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