The Proof You Can See

You don't need algebra to believe Pythagoras. Draw a square on each side of a right triangle.

The square built on the hypotenuse has exactly the same area as the two smaller squares combined. Cut those two smaller squares into pieces and you can rearrange them to fill the big one perfectly, with nothing left over and no gaps. This theorem has been proven in hundreds of different ways — even James Garfield, a U.S. congressman before he became president, published one.