Golden Rectangle Observation

Below is a special rectangle, called the Golden Rectangle. Points A and B can be dragged. Watch what happens when the size of the rectangle changes.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Questions to think about:
1. ABCD is a rectangle, but what shape is quad. AEFD? Look at the side measures. What about EBHG? In fact, how many of those shapes do you see? Can you figure out the pattern?
2. Do the following calculations: AB/AD, AD/EB, EB/GF, GF/IH, and IH/KJ. What happened, interestingly? If you had to guess, what do you think KJ/ML will be?
3. The ratio [1+sqrt(5)]/2, which is about 1.618, is called the Golden Ratio in mathematics. Why do you think this is called the Golden Rectangle? Do you think this is the only rectangle that does this? Why or why not?

Brian Bisignani, Created with GeoGebra