Introduction: Folding Paper Into Thirds

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.

Step 2:

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STEP 2
Fold the top piece in half about the major and minor axes to find the center point.

Step 3:

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At this point you may like to secure the two pieces of paper together with masking tape.

STEP 3
a) Draw two lines from the center point to the bottom corners (marked in green).
b) The red lines drawn from the intersection of the green lines and the meeting page edges indicate the third folds.

Step 4: Proof

Picture of Proof

For those of you that don't believe me.

I hope this will be of some use.

Have a nice day :)

Comments

cirano (author)2016-08-23

Thanks. Finally found a way to fold an A4 letter into exact thirds without the use of a ruler. (or the trial and error method)

stechi (author)2013-08-04

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)stechi2013-08-05

You got it :)

rimar2000 (author)2013-08-04

Interesting, thanks for sharing.

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