This proof of the Pythagorean Theorem was discovered by President J. A. Garfield in 1876 (T. Pappas,The Joy of Mathematics, p200, Wide World Publishing/Tetra, 1989). It is a variation on other proofs.
The key is the formula for the area of a trapezoid - half sum of the bases times the altitude - (a+b)/2 * (a+b). Looking at the picture another way, this also can be computed as the sum of areas of the three triangles - ab/2 + ab/2 + c*c/2. Simplifications yield a^2+b^2=c^2.
Click to view another Pythagorean Proof...animated!
