Chapter 4.3, Problem 22MS

Golden triangles. Draw a right triangle with one leg twice as long as the other leg. This triangle is referred to as a Golden Triangle. Suppose that one leg has length 1 and the other has length 2. What is the length of the hypoten use? Next draw a line from the right angle of the triangle to the hypotenuse such that the line is perpendicular to the hypotenuse. Now cut up the larger of the two new right triangles into four triangles (see Mindscape 20, “Cutting up triangles”). Show that all five triangles are the same size and are Golden Triangles. We will use this neat cutting up of the Golden Triangle in Section 4.4, “Soothing Symmetry and Spinning Pinwheels.”