The idea is that a square of side is cut from a corner of a square of side . By cutting the remaining figure in two and rearranging the pieces, a rectangle with side lengths of and can be formed, thus proving that .

Again, this is a simple construction that only requires paper, scissors, and a little guidance from the teacher so that students can discover this formula for themselves.

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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