Dilative rotation
A dilative rotation is a plane transformation that combines a rotation and dilatation with the same center.
It is similarity and, therefore, affinity.
Moving the indicated points we can change the position of the origin and destiny of the transformation applied to the logo of the Congress of Mathematics celebrated in Madrid in 2007. The logo by itself is an example to show the dilative rotation.
A plane tranformación does not have to be seen as a continuous transformation. Nevertheless, for that they wish it, the animation will show this.
Three possible ways set out. Combining rotation and expansion or expansion and rotation we showed the conmutatividad of the decomposition. The third option shows a continuous dilative rotation. In this case the trajectory of a point is an equiangular spiral arc.
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Multiplying two complex numbers
We can see it as a dilatative rotation.
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