Chapter 4.3, Problem 17MS

Do we get gold? Let’s make a rectangle somewhat like the Golden Rectangle. As before, start with a square; however, instead of cutting the base in half, cut it into thirds and draw the line from the upper right vertex of the square to the point on the base that is one-third of the way from the right bottom vertex. Now use this new line segment as the radius of the circle, and cont inue as we did in the construction of the Golden Rectangle. This produces a new, longer rectangle, as shown in the diagram. What is the ratio of the base to the height of this rectangle (that is, what is base/height for this new rectangle)? Now remove the largest square possible from this new rectangle and notice that we are left with another rectangle. Are the proportions of the base/height of this smaller rectangle the same as the proportions of the big rectangle?