In folding an irregularly shaped tent, I managed to get the shape of a triangle, which was evenly thick. Unfortunately, the best way to fold a tent is in a rectangle that is evenly thick. How can I fold a triangle into a rectangle without making some parts of it thicker than others?

This is an easy one but still great. Here is a proof for the method given.

The first fold is parallel to the base. Since the vertex now touches the other side, this fold is equidistant from that vertex as it is from the other side.

Due to similar triangles, the fold is half the area of the base, and its height (from the triangle's base) equals half the triangle's height. So its area is half the triangle's area.

In addition, the first fold's intersection with the two sides bisects both of them. Due to this and the first fold's length being half of the base, one can fold the two remaining corners so the sides touch, to form a rectangle.

Posted by Gamer on 2007-10-08 19:52:25