The Golden Rectangle and Logarithmic Spiral

Push the play button to see the animated construction.

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

Why is this called the Golden Rectangle and not the Golden Square?
If you had to construct this, what steps would you take?

Megan Urbanik, 1 November 2013, Created with GeoGebra