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:
“For a woman to get a rewarding sense of total creation by way of the multiple monotonous chores that are her daily lot would be as irrational as for an assembly line worker to rejoice that he had created an automobile because he tightened a bolt.”
—Edith Mendel Stern (1901–1975)
“The lazy manage to keep up with the earth’s rotation just as well as the industrious.”
—Mason Cooley (b. 1927)