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)

    If my sons are to become the kind of men our daughters would be pleased to live among, attention to domestic details is critical. The hostilities that arise over housework...are crushing the daughters of my generation....Change takes time, but men’s continued obliviousness to home responsibilities is causing women everywhere to expire of trivialities.
    Mary Kay Blakely (20th century)

    The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.
    Charlotte Perkins Gilman (1860–1935)

    Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, square dancing...?
    Mason Cooley (b. 1927)

    Look at this poet William Carlos Williams: he is primitive and native, and his roots are in raw forest and violent places; he is word-sick and place-crazy. He admires strength, but for what? Violence! This is the cult of the frontier mind.
    Edward Dahlberg (1900–1977)