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Why does paper fold so well?

bbc.co.uk

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Re: Why does paper fold so well?

#21

Post by rusk »

srean wrote: post #6

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 geometrica…

The shortest distance between two points is a straight line?

A sheet of paper approximates a Cartesian plane probably more closely than most things we can fold

Therefore a fold will always be in line with the theoretical 2D plane and thus will be the shortest (straight) line.

Re: Why does paper fold so well?

#22

Post by srean »

globular-toast wrote: post #20
srean wrote: post #6

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 geometrica…

> In fact I don't know of any other good way of obtaining a straight edge from scratch quickly A string made taut between two points is surely a better way? And works at much bigger sizes too (people build walls and foundations using this technique all the time). The paper is less useful in practice because any paper you find is probably straight and square anyway. Still, I had fun thinking about this as I definitely…

I have an asterisk in my post addressing that :) Happy to have picqued your mind.

BTW, your method was the method of choice for the surveyors of the Nile, from the Egyptian civilization.

Paper is hi-tech and was not available until much later, and as you mentioned doesn't scale. But if I have misplaced my ruler ...

Re: Why does paper fold so well?

#23

Post by anax32 »

srean wrote: post #17
roelschroeven wrote: post #15

Earlier quoted context omitted.

And once you have created such a straight line, you can fold the paper again such that the first crease lines up on both sides of the new crease, and then you have a right angle.

Indeed ! One can create an axiomatic system of geometry through such coincident folds (as an alternative to straight-edge and compass) and it turns out to be more powerful than the Euclidean system. One can construct cube roots, trisect angles. Depending on the choice of paper folding axioms one can go beyond cube roots and k-secting angles to the entire set of algebraic numbers. https://en.wikipedia.org/wiki/Huzita%…

I'm not getting any work done today

thank you!

Re: Why does paper fold so well?

#25

Post by srean »

anax32 wrote: post #23
srean wrote: post #17

Earlier quoted context omitted.

Indeed ! One can create an axiomatic system of geometry through such coincident folds (as an alternative to straight-edge and compass) and it turns out to be more powerful than the Euclidean system. One can construct cube roots, trisect angles. Depending on the choice of paper folding axioms one can go beyond cube roots and k-secting angles to the entire set of algebraic numbers. https://en.wikipedia.org/wiki/Huzita%…

I'm not getting any work done today thank you!

LoL. Most welcome.

My best (worst) HN days are like that :)

Re: Why does paper fold so well?

#26

Post by gruez »

Peterz_shu wrote: post #24

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.

But you can fold aluminum foil just fine? That certainly doesn't have "a lot of air gaps within its fiber"

Re: Why does paper fold so well?

#27

Post by wongarsu »

srean wrote: post #6

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 geometrica…

If you want to use a rope to get a straight line, your best bet is to turn the rope itself into the pencil. Coat it in chalk or other powder, then put it under tension and snap it on to the desired surface

Re: Why does paper fold so well?

#28

Post by bena »

wongarsu wrote: post #27
srean wrote: post #6

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 geometrica…

If you want to use a rope to get a straight line, your best bet is to turn the rope itself into the pencil. Coat it in chalk or other powder, then put it under tension and snap it on to the desired surface

This is actually a tool used in construction. A chamber filled with chalk and a coiled line. You hook the line to one end of your item, pull the chamber across, make it tight, snap the line.

https://www.homedepot.com/p/Milwaukee-100-ft-Bold-Line-Chalk...

Re: Why does paper fold so well?

#30

Post by dotancohen »

globular-toast wrote: post #20
srean wrote: post #6

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 geometrica…

> In fact I don't know of any other good way of obtaining a straight edge from scratch quickly A string made taut between two points is surely a better way? And works at much bigger sizes too (people build walls and foundations using this technique all the time). The paper is less useful in practice because any paper you find is probably straight and square anyway. Still, I had fun thinking about this as I definitely…

Over long distances the string will sag in the middle. That's one of the reasons (not the only reason) construction uses lasers today.
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