Wrapping an Equilateral Triangle (Posted on 2005-10-10)

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?

The smallest square has sides of 3/(1+sqrt(3)) = 1.0981.
One vertex of the triangle is on the midpoint of a side of the square and the opposite side of the triangle is parallel to a side of the square.

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