Paper Divisions - Fifths, thirds, sevenths, etc...

Hello Everybody, I am Tadashi Mori and in this video you'll learn a little bit about paper divisions, so you'll have an advanced lesson about the mathematics involving origami. So, let's start. First, let's remember how to divide the paper in three parts. So, fold the side of the paper in two parts now, make a fold from the vertex up to this line, and fold the diagonal. So, this point here is exactly one third of the paper. And, actually, you can keep doing this to find other divisions. Using the 1/2 mark, you can find 1/3. Using the 1/3 mark, you can find 1/4. And using this mark, you can find 1/5, and so on. So, suppose you want to divide the paper in 9 parts. First, divide the side of the paper in 8 parts, then apply the same method once and you have 1/9. You can also reverse this method. So, divide the diagonal in 4 parts, and make a fold passing through this point. Now you have 1/3 of the side of the paper. So, you have two techniques. One that divides the paper in one more part, and the other that removes one division from the paper. Using these two techniques you can divide the paper by any natural number. The problem is... If you fold too much the folds will get less and less precise. So, you can also divide the paper in 5 parts like this. Make a fold from the vertex to the middle point of the other side of the paper, then, fold the side of the paper up to the tip of the first fold. Like this. The first technique works because we have two similar triangles. By following these equations you can see that the side is now divided by n+1 For the second technique, I couldn't think of an easier way to explain why it works, So, if you know, please make a video response showing how to do it. The idea of my explanation is to find the tan(y) using some trigonometric identities. And after you find that the tan(y) is 4/3 you just apply the fact that these two triangles are similar. So, you find that "a" equals 2/5 of the side of the paper. So, that't it! I hope you enjoyed this video, and Thanks for watching! See you! Bye Bye!