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Picture of Folding Paper into Thirds
I came across an article on Make on how to fold a piece of paper into thirds. I thought the technique was cool, but the third marker point is at a rather strange location on the page, making it hard to fold the page.

I decided to dive deeper into the subject of mechanical construction and dividing a straight line into equal segments. The applet shows you how to use a ruler and a compass to divide a line into N segments. I still wasn't happy with this technique because it requires multiple tools and the lines go off the page. 

From the mechanical construction technique I noted that a reference line is created of arbitrary length. The line is created by drawing N segments and then projecting this onto the line we are trying to divide. This tutorial uses a similar technique, but using the paper itself as the line segments. You might find this useful, so take a look!


Step 1:

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You can do this with two A4 pieces of paper, or a single A3 piece. If you don't mind getting additional folds on your page you can use A3, but I am going to take you through this with A4 paper.

STEP 1
Line up the pages along the long end.

 
stechi2 years ago
It's amazing what you get on here! Took me a while, but the proof makes sense if you spot it's similar triangles with side lengths L/2, 3W/2 and X, W/2. The ratios of the sides are the same.
puffin_juice (author)  stechi2 years ago
You got it :)
rimar20002 years ago
Interesting, thanks for sharing.