Dilative rotation

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.

LINKS

	Equiangular spiral In an equiangular spiral the angle between the position vector and the tangent is constant.
	Dilation and rotation in an equiangular spiral Two transformations of an equiangular spiral with the same general efect.
	Multiplying two complex numbers We can see it as a dilatative rotation.
	The golden ratio From Euclid's definition of the division of a segment into its extreme and mean ratio we introduce a property of golden rectangles and we deduce the equation and the value of the golden ratio.
	The golden spiral The golden spiral is a good approximation of an equiangular spiral.
	The golden rectangle and two equiangular spirals Two equiangular spirals contains all vertices of golden rectangles.
	The golden rectangle A golden rectangle is made of an square and another golden rectangle.
	The golden rectangle and the dilative rotation A golden rectangle is made of an square an another golden rectangle. These rectangles are related through an dilative rotation.