This was certainly not the introduction my geometry teacher gave on the day we started studying two-column proofs.

However, even in our formal geometry and honors geometry classes, we still tend to largely ignore the "two-column" proof. By the time I'd left the 9th grade, I could do 2-column proofs in my sleep.

For centuries, students have learned that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Known as the Pythagorean Theorem, this ...