Continued Fraction - Generalized Continued Fraction For Square Roots

Generalized Continued Fraction For Square Roots

The identity

(1)

leads via recursion to the generalized continued fraction for any square root:

(2)

Read more about this topic:  Continued Fraction

Famous quotes containing the words generalized, continued, fraction, square and/or roots:

    One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.
    —H.L. (Henry Lewis)

    There is not any present moment that is unconnected with some future one. The life of every man is a continued chain of incidents, each link of which hangs upon the former. The transition from cause to effect, from event to event, is often carried on by secret steps, which our foresight cannot divine, and our sagacity is unable to trace. Evil may at some future period bring forth good; and good may bring forth evil, both equally unexpected.
    Joseph Addison (1672–1719)

    The visual is sorely undervalued in modern scholarship. Art history has attained only a fraction of the conceptual sophistication of literary criticism.... Drunk with self-love, criticism has hugely overestimated the centrality of language to western culture. It has failed to see the electrifying sign language of images.
    Camille Paglia (b. 1947)

    If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would of itself be venerable enough. But having only imaginary knowledge, they must employ those silly tools that strike the imagination with which they have to deal; and thereby, in fact, they inspire respect.
    Blaise Pascal (1623–1662)

    People who wish to salute the free and independent side of their evolutionary character acquire cats. People who wish to pay homage to their servile and salivating roots own dogs.
    Anna Quindlen (b. 1952)