You have an equilateral triangle you want to wrap with a square piece of paper. If the triangle has unit sides, what is the smallest square piece of paper that can be folded around the triangle such that both the front and back sides of the triangle are completely covered by the paper?

I think Ady's solution is wrong, though I can't really tell without a better description of his solution.

The answer 1/cos(15) seems to mean that he rotated a triangle 15 degrees and inscribed it in the smallest square.  Find 15 degrees hard to visualize?  I did too until I realized that one of the triangle's corners is pointing directly NE, and coincides with one of the square's corners.  The smallest square that will fit around this has a side of 1/cos(15), and it will touch all three corners.

Why does this not work?  If you think about the corner pointing NE, it is 60 degrees.  But the most paper we can fold onto this corner is 30 degrees worth (90 - 60 = 30).It doesn't work.

I believe that in order to be able to fold the square over the triangle, you will have to make the square bigger, so that the triangle's NE corner no longer touches the square.

I hope to post my own solution soon.

Posted by Tristan on 2005-10-12 16:11:55