Golden Rectangles & the Logarithmic Spiral

You may press the "stop" button to pause the animation and then drag the green dot by hand to go through the construction steps. Try doing this both with and without the spiral showing.

Ask yourself the following questions:
1. Why would the logarithmic spiral be related to the golden ratio? (Think about this and then perhaps research it on the internet.)
2. What would happen with the spiral if the golden rectangles pattern was continued and we zoomed in to get a more close-up look?

Nathaniel Lovelady, 4 November 2013, Created with GeoGebra