The golden rectangle and the dilative rotation
When we divide a golden rectangle in a square and another golden rectangle this new rectangle is similar to the initial. A dilative rotation transforms one into the other.
We can see that dilative rotation in three ways: a rotation followed by an expansion, an expansion followd by a rotation or a continuous dilative rotation. In this case, the vertices follow two equiangular spirals.
Four straight lines contain all the vertices of the rectangles. These four straight lines concur in a point. This one is the center of the transformation. The angle of the turn is a right angle and the homotetic reason is the inverse of the golden number.
REFERENCES
Coxeter - Introduction to Geometry (John Whiley and sons)
