Folding an Equilateral Triangle

There are more common and, it has to be said, simpler ways of folding an equilateral triangle from a rectangle. But this method makes use of the unique properties of “A” paper.

The first stage is to make a “measuring piece” that will be used to find out where to fold the rectangle.

Fold a rectangle in half along its diagonal.

This fold has a length of √3. ( Check this using Pythagoras’ Theorem)

Now take this new shape and fold in the end so that fold passes through the first peak.

Repeat this with the other end of the diagonal and you will find that the original diagonal has been divided into 3 equal parts. The length of the base

is now √3/3

Is this just roughly correct or can you prove that this method of folding does indeed exactly trisect the diagonal of the “A” rectangle?

Take another sheet of A paper equal to the original.

Place the “measuring piece” alongside and use it to measure off where the fold must come. Mark and crease.

Repeat on the other side using partly unfolded “measuring piece”.

Having scored along the creases, fold to give an equilateral triangle.

This creates an equilateral triangle of height 1 unit. In fact it is the largest equilateral triangle that can be created from this rectangle.

For patterns and tessellations with this triangle click here