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)
LINKS
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The golden spiral
The golden spiral is a good approximation of an equiangular spiral.
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Dilative rotation
A Dilative Rotation is a combination of a rotation an a dilatation from the same point.
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The golden rectangle and two equiangular spirals
Two equiangular spirals contains all vertices of golden rectangles.
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Equiangular spiral
In an equiangular spiral the angle between the position vector and the tangent is constant.
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