The golden rectangle and two equiangular spirals
We can see that some vertices of the golden rectangles of this construction are in a equiangular spiral.
Coxeter ask to prove ("Introduction to Geometry?, p 196) that the other vertices also are in another equiangular spiral.
We can get this spiral by means of an expansion of the initial golden spiral or by means of a rotation.
In one animation we can see the dilatation that takes an spiral into the other.
In the second animation we can see the rotation that transforms an spiral into the other.
REFERENCES
Coxeter - Introduction to Geometry (John Whiley and sons)
LINKS
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Dilation and rotation in an equiangular spiral
Two transformations of an equiangular spiral with the same general efect.
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The golden spiral
The golden spiral is a good approximation of an equiangular spiral.
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