The number is called the golden mean. The ancient Greeks felt that a rectangle whose side...

The number is called the golden mean. The ancient Greeks felt that a rectangle whose sides were in the ratio 1 to τ was the most esthelically pleasing. Such a rectangle is called golden. Hence, for example, each side of the Parthenon, a large rectangular building dating to 435 B.C., is a golden rectangle. Suppose you remove a 1 × 1 rectangle from a golden rectangle as shown. Show that the rectangle that remains is also golden.