The Origami Forum

I try to fold the sea turtle. Base is 10*10 grid line . I used to fold only 1/2 devided into 8 lines ,16 lines. and 32 lines. But how about the techinc, if the pattern is not devided into half. Now I used ruler to measure the paper and devide into 1/10. However I believe that this method will not be practical if I fold the very big paper. Do you have any other theory?

You can divide the paper into fifths, then further divide by two to get the 10x10 grid.

This article should help you divide paper into 1/5ths:
http://www.origami.gr.jp/People/CAGE_/divide/04-e.html

If you write your grid number as a product fo prime numbers, you can easily see how you have to divide it. In this case 10= 2*5 (like eric_son already mentioned).
You can do this for any number eg 24=2*2*2*3. This tells that you should first divide in 3, an then each third in 8 (=2*2*2).

The easiest way is to divide the paper to 16x16 and cut the edges.

Note:
It makes the paper smaller!
You can't use this method for asymmetric grids (ex: 10x13)

The first step to getting the desired grid is to take the grid number you want and then break it down into the prime factorization. Then you divide your own paper based on the prime factorization like Brutus said. But which method to use to divide the paper into desired sections is the question...

~I don't like the method where you have to cut the paper to get the neccessary grid you want because that really wasts paper. I would only do that if I had to get a 63 by 63 grid or something (not likely!).

~I don't like the method using mathematics to get a grid because whenever I try those methods, I can never get it perfect. If the mathematic way works for other people, thats fine- I just can't get it very well.

After experimenting with all other methods I know of (including measuring the paper and marking off points), the method I like most is the guess-and-check method (at least thats what I call it). The guess-and-check method, although having a name that drives off many folders, is more of systematically reducing the margain of error while folding to end up with perfect measurements.

Page 10 of Robert Lang's article has a great diagrams of using the guess-and-check method to get perfect 3rds, as well as an explanation of how and why it works (I just skip over the explanation because it has too much complicated math stuff).
*Note: Just for reference, figures 10 and 11 on Robert Lang's essay have mathematicall ways to divide the square into fifths.

Guess and check works well enough for thirds and fifths. But once you get any higher it becomes really difficult. Try guess-and-check on 13ths...

Another way that works really well is the method Marc Kirschenbaum uses in his chess board (diagrams at origami.com) The only problem is that as it's diagrammed, you end up with an extra crease or two on your paper (and not a useful one like the diagonal). You can, with experience, pull it off without the extra creases, but it's much harder to get it right..

It should work- I've used the guess and check method for 11th and 13ths divisions before.

there are a lot of ways how to divide paper into a number of parts.

this is the way i always divide paper.

1. What is the number of parts you want to divide into?
2. Take n-1 and divide the paper in so many parts. So for dividing into 5 you need to divide into 4 first.
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3. Now take the lower right point, and take it to the 3/4th mark (or 4/5th or whatever you want)
4. Fold the upper left point to the intersection with the folded paper.
5. Unfold it all.
6. The fold you made in step 4 is 1/5th (or whatever you want)