The Origami Forum

Hi,
I am designing a model, and its references lie on a 13x13 grid. Does anyone know of a folding sequence to get this grid?
Many thanks,
Justin

Here you go

Of course you can always use ref finder but i like this solution more.

Is it proven that there is (or not) a folding sequence to get any N x N grid, where N is a prime number ?
Just wondering...

Thanks Djorde!

It is possible to divide any given line into any division you like with the method shown here: http://www.origami.at/diagrams/Fifths.pdf
For 13th just imagine that you have 6/13th on one and 7/13th on the other side.

Lol ok, I guess it's a practical solution
But it's cheating imo...
If you want perfect precision, you will always get closer to it, but you'll never reach it.
And for a relatively big prime number, at the scale of origami (let's say, 47) it's gonna be a torture.
I personnally wouldn't put this method in any diagrams :p

It is more precise than most other methods. With just one iteration the error gets so minor that it is near to non-existent, even if you start by dividing in half (the only exception being thirds where you need some more iterations). Furthermore, the higher the number gets the smaller the error. So 47th would be very very precise. The method is a proven mathematical solution, that is very easy to remember and has nothing to do with cheating. Getting absolute precision in Origami is an impossible thing to achieve non the less. Apart from paper thickness, hard to see lines and other factors, people just aren't able to get absolute precision. What you get with this method is as good as you can get and can well compete with several other methods when it comes to accuracy.

Edit: Here is a pretty good paper by Robert J. Lang explaining the method and its accuracy in great detail and with mathematical proofs: http://www.langorigami.com/science/math ... ctions.pdf

Ok, that's not what I meant
I'm sure it works very well, and I think I know why, but by "a torture", I didn't mean "inefficient", but "very laborious".
And if I call this cheating, it's because, from a geometrical point of view, you don't get exact values.
I'm looking at the mathematical approach here, not the practical folding.
And actually, given the fact that referenceFinder itself rarely gets you exact values, I wouldn't be surprised if finding a method that would get you perfect precision for any grid size (without any approximation) was just plain impossible.

I use the method that Anna pointed out earlier with the 5ths. I find it to be pretty dang accurate no mater what grid I fold from it.

Say you wanted to fold a 37 grid.
*Find 0, 5/32 (because 32 is the next smallest power of 2, and because 37 - 32 = 5) and connect that with 1,0.
*Connect 0,0 with 1,1.
*Those two creases cross the paper at 5/37 of the diagonal, which translates to the equivalent distance along the edge.

There are other methods that give a cleaner result, but they're more work than I care to put into use.

This will hopefully explain how to get any division better: http://m.flickr.com/#/photos/langko/7811864300/
As for 13ths: http://m.flickr.com/#/photos/langko/7666732554/

Yes, this kind of division is part of the Haga Theorem (see page 6):
http://www.origami.gr.jp/Archives/Peopl ... /01-e.html
http://www.origami.gr.jp/Archives/Peopl ... /02-e.html
http://www.origami.gr.jp/Archives/Peopl ... /03-e.html
http://www.origami.gr.jp/Archives/Peopl ... /04-e.html
http://www.origami.gr.jp/Archives/Peopl ... /05-e.html
http://www.origami.gr.jp/Archives/Peopl ... /06-e.html
It works good but always leaves unnecessary crease marks.

This is exactly what I was looking for.
Thanks ! ^^

There's also the method outlined by Jared, it's probably the one I use most often and works for all sorts of weird divisions like 11ths, 13ths, 31sts and so on. http://www.flickr.com/photos/oriholic/4 ... ist-galen/

Quach asked me to post this.