Dilatación y giro de la espiral equiangular
"This curve was first recognized by Descartes. Jacob Bernouilli found it so fascinating that he arranged to have it engraved on his tombstone with the inscription
These words ("Though changed I shall arise the same") express a remarkable consequence of the way the curve can be shifted along itself by a dilative rotation: any dilatation has the same effect on it as a rotation, and vice versa." (Coxeter)
When pressing the button "Animation" takes place a transformation of the spiral. Is a turn or an dilatation?
REFERENCES
Coxeter - Introduction to Geometry (John Whiley and sons)
Steinhaus - Mathematical Snapshots.
LINKS
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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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Equiangular spiral
In an equiangular spiral the angle between the position vector and the tangent is constant.
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The golden rectangle and two equiangular spirals
Two equiangular spirals contains all vertices of golden rectangles.
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