Joel Cooper - Masks

redheadorigami · Post by **redheadorigami** » May 24th, 2010, 12:01 pm

thirty- ninths??

Growlanator · Post by **Growlanator** » May 24th, 2010, 8:43 pm

redheadorigami wrote:thirty- ninths??

western pond turtle from Origami Design Secrets has 39ths and 78ths, my first fold was terrible so I am going to refold it at some point

redheadorigami · Post by **redheadorigami** » June 7th, 2010, 8:06 am

Im serious, guys.

<-------my serious face

chesslo · Post by **chesslo** » June 7th, 2010, 11:30 am

What are you talking about?

redheadorigami · Post by **redheadorigami** » June 7th, 2010, 1:04 pm

Im talking about the guys figuring out the algorithms or something to fold them into: 5ths, 7ths, elevnty sevenths and 39ths!

bethnor · Post by **bethnor** » June 7th, 2010, 4:41 pm

in my honest opinion, with 39ths, you are really better off just measuring and dividing.

an easy way to approach this is to cut a square that is 39 cm/58.5 cm/78 cm to a side.

i'm a little bit of a purist myself, but after awhile it just gets aggravating.

Post by **origami_8** » June 7th, 2010, 5:04 pm

39ths are 13ths divided into 3rds. A bit tedious to fold.
Another way to do this would be to fold 40ths (5ths divided into two 3 times) and cut off one square from two adjacent edges. This way you loose a tiny bit of paper but it is far easier to fold.

However, I'm a purist, therefore I would take the first approach.

Jonnycakes · Post by **Jonnycakes** » June 7th, 2010, 5:46 pm

13ths divided into thirds is indeed tedious-and inaccurate. It is best to divide straight into 39ths, since there are no smaller binary divisions. Here is how to divide into 39ths with the Haga theorem:

origamimasterjared · Post by **origamimasterjared** » June 7th, 2010, 10:03 pm

For any odd number, fold directly to that division. Prime factorization isn't really useful.

This is a little study I did on the method I like to use. It proves it and shows a bunch of examples, along with how to go from the wanted division to the necessary reference points and vice versa.

[img]http://farm3.static.flickr.com/2501/4145188320_fd5507ec5b_b.jpg[/img]

39 is more than 32, so it is a bit painful--you will have to use 64ths in this method.

39-32 is 7, so you'll want to find the 7/39 line to make your 39ths grid. Then you can easily divide the 32/39 into 32. In the equations above, x is the position you want, and y is the position you need to use to find it.

y = (x-1/2)/(x-1) = (7/39-1/2)/(7/39-1) = 25/64

That's the true math behind it, but calculating the point you need is actually much easier. Just do 64-39=25 and you will realize that you just need 25/64!

So 25/64 is our reference point

The top of this page shows how to use this method.

This is my favorite method, because, while it requires a 1-level higher order of reference lines (64 vs 32 in this case) the crease you make always divides the square in half by area, and also gives you two points that you want. (both ends of the crease). Then if you fold those points to each other, you will have two points the other way. Enough to make the grid both directions. And finally, unlike crossing diagonals, this leaves the interior of the square clean, though this is a minor issue.

bethnor · Post by **bethnor** » June 7th, 2010, 10:09 pm

a long time ago, i took multi-variable calculus and did quite well in it.

it's obvious by reviewing the last few posts that it was really a long time ago.

origamimasterjared · Post by **origamimasterjared** » June 7th, 2010, 10:19 pm

Haha, it's just subtraction! For my method, you just go up to the next power of 2 (2, 4, 8, 16, 32, 64) and subtract the number of divisions you want. Then put that number over the power of 2.

For 39ths: 64-39=25 ---> 25/64

chesslo · Post by **chesslo** » June 8th, 2010, 6:25 am

My try of the Mask!:)

Origamist388 · Post by **Origamist388** » June 8th, 2010, 6:35 am

Looks nice!