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)

    The protection of a ten-year-old girl from her father’s advances is a necessary condition of social order, but the protection of the father from temptation is a necessary condition of his continued social adjustment. The protections that are built up in the child against desire for the parent become the essential counterpart to the attitudes in the parent that protect the child.
    Margaret Mead (1901–1978)

    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)

    This house was designed and constructed with the freedom of stroke of a forester’s axe, without other compass and square than Nature uses.
    Henry David Thoreau (1817–1862)

    The Plains are not forgiving. Anything that is shallow—the easy optimism of a homesteader; the false hope that denies geography, climate, history; the tree whose roots don’t reach ground water—will dry up and blow away.
    Kathleen Norris (b. 1947)