Periodic Continued Fractions
A regular periodic continued fraction consists of a finite initial block of partial denominators followed by a repeating block; if
then ΞΆ is a quadratic irrational number, and its representation as a regular continued fraction is periodic. Clearly any regular periodic continued fraction consists of restricted partial quotients, since none of the partial denominators can be greater than the largest of a0 through ak+m. Historically, mathematicians studied periodic continued fractions before considering the more general concept of restricted partial quotients.
Read more about this topic: Restricted Partial Quotients
Famous quotes containing the words periodic and/or continued:
“But parents can be understanding and accept the more difficult stages as necessary times of growth for the child. Parents can appreciate the fact that these phases are not easy for the child to live through either; rapid growth times are hard on a child. Perhaps its a small comfort to know that the harder-to-live-with stages do alternate with the calmer times,so parents can count on getting periodic breaks.”
—Saf Lerman (20th century)
“The problems of society will also be the problems of the predominant language of that society. It is the carrier of its perceptions, its attitudes, and its goals, for through it, the speakers absorb entrenched attitudes. The guilt of English then must be recognized and appreciated before its continued use can be advocated.”
—Njabulo Ndebele (b. 1948)