In mathematical theory of dynamical systems, an irrational rotation is a map
where θ is an irrational number. Under the identification of a circle with R/Z, or with the interval with the boundary points glued together, this map becomes a rotation of a circle by a proportion θ of a full revolution (i.e. an angle of 2πθ radians). Since θ is irrational, the rotation has infinite order in the circle group and the map Tθ has no periodic orbits. Moreover, the orbit of any point x under the iterates of Tθ,
is dense in the interval [0, 1) or the circle.
Read more about Irrational Rotation: Significance
Famous quotes containing the words irrational and/or rotation:
“How did reason enter the world? As is fitting, in an irrational way, accidentally. We will have to guess at it, like a riddle.”
—Friedrich Nietzsche (18441900)
“The lazy manage to keep up with the earths rotation just as well as the industrious.”
—Mason Cooley (b. 1927)