The Origami Forum

how do you divide a peice of paper into 13ths?

Using ruller. You can for example fold 15 cm square by 1 cm and then 2 cm cut on each size... Or divide it on 16th by precreasing and cut 3 cm on each side - for this, you do not need a ruller.

I would also use the 16ths method, and trim off 3 squares

But this thing called a "ruler". It's a long rectangular thing that can either be made of wood, plastic or metal. You can buy it in most stationery shops. the amazing thing is that it has little LINES and NUMBERS printed on them! You can actually use this amazing invention to measure the length of an object! Now, place the ruler on top of the paper and measure it out. Take the length of the paper and divide it by 13. Measure out this brand new number onto the paper, mark it out and fold the paper over the mark. Congratulations!!! You have just divided the paper into 13ths!!!

Okay, just joking. Or maybe I'm not. Sorry, but the only way to divide it into 13ths, (which is a very unfriendly origami number) is by measuring with a ruler, or by folding out a simpler grid and cutting out the excess paper. If there are any other ways, then I don't know about them, because I'm a moron. Why do you need a 13 by 13 grid anyway? Are you trying to make an origami cat out of black paper and use it to curse your enemies?

Of course there's always Haga and related theorems:

http://origami.gr.jp/People/CAGE_/divide/index-e.html

Your square extends from 0 to 1 along the horizontal, and 0 to 1 on the vertical. Make a line from the (0,1) to (1,0) (Diagonal from top left to bottom right.) Now make a line from (0,0) to (5/8,1). Where these two cross is 5/13 along the diagonal.

By the way, this method will work on any rectangle.

If i remember correctly, lang fiddler crab needs a 13*13 (26*26) grid. Of course, i would use reference finder point (0,1/13)

Actually, Sebastian, 5/13 (or 8/13) is a better choice. That way, you have the crease with a large amount of paper on either side, making it easier to fold accurately. Also, this leaves you so that one side needs to be divided into 8ths, which is easy. 4/13 (or 9/13) would also work well.

There is a pattern I've seen for dividing paper into odd proportions like this.
1. Divide one edge into twelfths, just making reference points.
2. The tricky part! Make a line that goes from a corner opposite the twelfths to one the last twelfth on that same edge.
3. Fold the diagonal, and where the tricky line and the diagonal intersect should be at 1/13.

I didn't try this myself yet, but I think it will work.
This method works for most odd proportions: Subtract 1 from the total needed, and follow the steps, changing the "twelfth" part to n-1.

Yes. it is the best way to divide the paper into 13th Lephantome92. I saw this from how to divide in to 3rd, you half it first, then do the method.
I also saw how to make 5th. You just divide in to 4th and then do the method, but fold the corner to the below-the-half crease.
So, I can say that you can divide paper in to ANY division of the paper.
You just need some Mathematical knowledge, the HCF (Highest Common Factor).
I hope you could understand what I have said so far.

there's a pretty easy way to devide a square into 13th.
I made a picture for you.


(thanks to reference finder)

In case somebody is interested, I explain a little First Haga Theorem in the last entry of my blog, I leave you the link:

http://origamido-en.blogspot.com/

I apologyze in advance for any english language mistake

many regards.

Jared and TheRealChris's methods are most elegant,

but there are two other ways: the n+1 method that works with the diagonal and the intersection of an edge and the n-1 method (already aforementioned) that works with marking the edge and intersecting the diagonal.

THE N+1 METHOD

General form: if you want to divide the paper in n'ths you get 1/n by marking 1/(n+1) on the diagonal. Then fold from this mark to the opposite corner. Extend the crease to the opposite edge. It crosses the edge at 1/n. With n e



So if you want to fold into thirds mark 1/4 of the diagonal's diagonal. Let's say this 1/4 of the diagonal is at the lower left corner (what I usually do) then crease from the 1/4 of the diagonal to the lower right corner. Extend this crease to the left edge. Where it intersects the left ede is your 1/3

So if you want 1/5 with this technique mark off 1/6 of the diagonal.

So 1/13 goed like this:
- mark 1/8 of the diagonal
- extend a crease from this 1/8 to the lower right corner
- where it crosses the left edge is 1/7
- mark 1/14 of the diagonal (you could turn the paper 180 degrees to not get confused with the previous creases).
- Again extend the 1/14 to the right corner. Where this crease crosses the left edge there is your 1/13...


THE N-1 METHOD

General: to divide the paper into n'ths you get 1/n of the diagonal of the square by marking 1/(n-1) of the edge of the square. Then fold from that mark to the opposite lower corner. The crease intersects the diagonal at 1/n. With n e



So for 1/3 mark 1/2 of the left edge of the square. Now fold from this mark to the lower right corner. The crease intersects the diagonal coming from the lower left corner going to the upper right corner at 1/3.

So you get 1/13 by:
- Mark 1/2 on the left edge.
- Fold from this mark to the lower right corner.
- This crease intersects the diagonal at 1/3
- Now use this to get 1/12 on the left edge
- Fold from this new mark (you could turn the paper 180 degrees) to teh lower right corner.
- This new crease should intersect the diagonal at 1/13.