The Golden Rectangle and Logarithmic Spiral

Press the play button to see the logrithmic spiral and golden rectangle constructed.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions:
1. The golden rectangle is created from a square (the largest purple square), and then the rectaingle above it (containing all of the other squares) is formed to created one big rectangle (the whole shape). How do you think we can construct the small rectangle above from the square?

2. Uncheck the Logrithmic Spiral button. Without seeing the spiral, how is it created?

Dixie Christensen, 29 October 2013, Created with GeoGebra