Question

1+v5 1.618 is called the golden 12. The number t = 2 mean. The ancient Greeks felt that a rectangle whose sides were in the ratio 1 toT was the most esthetically 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. Sup- pose you remove a 1 x 1 rectangle from a golden rectan- gle as shown. Show that the rectangle that remains is also golden. 1

can you provide a good proof for this?

Answer 1

F :-1-→ et-> # area of rectangle - 1X0 = (goldean mean) sides of old tue'angle aui in ratione - § = 1115 zo .618 E -1+ # Nere mectangle is : Thus, ratio of sides is : coration date 13.-1 - 64 LEI Thus, rano y sides over e = Pinewoo late (nationalse) the = (475) - Limun golden, mean) new rectangle is also golden since sieles' are in golden mean ratoo