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?

(In reply to re: Solution? by Sing4TheDay)

Actually, his method will work for ANY triangle. Check it out.

I had a really long explanation to support Fletch's solution, but then I thought of a simplification.

Label the points of the triangle A B and C (how original, I know). If the triangle is obtuse, let A be the obtuse angle. Otherwise, it doesn't matter how you label the points (so in and isosceles triangle, point A doesn't have to be the corner between the two equal sides, as long as the triangle is not obtuse)

Draw a line from point A to line BC, perpendicular to BC. Call the intersection point P. Notice that triangle ABP and triangle ACP are both right triangles now.

Well, it was intuitive and easy to prove to ourselves that folding the two non-right angles in a right triangle into the right angle will form a rectangle of even thickness. Now all we are doing is doing this to two right triangles.

I hope that cleared it up a bit. I know it wasn't a formal proof of his method, just an brief explanation on how it does indeed apply to all triangles, not just equilateral, isosceles, or right.

Edited on December 30, 2004, 6:46 pm

Posted by nikki on 2004-12-30 16:45:34