Chapter 4.3, Problem 13MS

Counterfeit gold? Draw a rectangle with its longer edge as the base (it could be a square, it could be a long and skinny rectangle, whatever you like, but we suggest that you do not draw a Golden Rectangle). Now, using the top edge of the rectangle, draw the square just above the rectangle so that the square’s base is the top edge of the rectangle. You have now produced a large new rectangle (the original rectangle together with this square sitting above it). Now attach a square to the right of this rectangle so that the square’s left side is the right edge of the large rectangle. You ‘ve constructed an even larger rectangle.

Now repeat this procedure—that is, append to the top of this huge rectangle the largest square you can and follow that move by attaching the largest square you can to the right of the resulting rectangle. Start with a small rectangle near the bottom left corner of a page and continue this process until you have filled the page. Now measure the dimensions of the largest rectangle you’ve built and divide the longer side by the shorter one. How does that ratio compare to the Golden Ratio? Experiment with various starting rectangles. What do you notice about the ratios?