The golden spiral
Drawing up an arc of circumference in each square we get a golden spiral.
These vertices also belong to an equiangular spiral
When studying the golden rectangle and dilative rotation also we can found that spiral.
"This true spiral is closely approximated by the artificial spiral formed by circular quadrants inscribed in the successive squares. (But the true spiral cuts the sides of the squares at very small angles, instead of touching them)" Coxeter.
Using the zoom we can see how the equiangular spiral cuts the sides of the squares. Dragging with the mouse right button we can move all the drawing. We can see (two different animations) how a dilative rotation transform one golden rectangle into another.
REFERENCES
Coxeter - Introduction to Geometry (John Whiley and sons)
