Golden Rectangles and Golden Spirals
A Golden Property
When you remove from a golden rectangle a square whose side length is equal to the shorter side of the golden rectangle, the remaining rectangle is a golden rectangle.
Explore the app below to create a sequence of nested golden rectangles and discover how to construct a golden spiral.
Points A and B are draggable, allowing you to verify the invariance of the construction.
Another Golden Property!
Use GeoGebra's tools (or recreate the construction on paper), then measure the ratio between the side lengths of two successive squares removed from the golden rectangle.
What number do you get?