Chapter 4.3, Problem 18MS

Do we get gold this time? (S) We now describe another construction of a different type of rectangle. It is exactly the same as the Golden Rectangle except that, instead of starting with a square, we begin with a rectangle whose base is twice as long as its height. Now connect the midpoint of the base to the upper right vertex with a line, and use this line as the radius of the circle and continue 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 new big rectangle (that is, what is base/height for this new rectangle)? Now remove the original rectangle. This gives us a new, smaller rectangle. Are the proportions of the base/height of this smaller rectangle the same as the proportions of the big rectangle? Experiment with starting rectangles of differing proportions.