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)

    “Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    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)

    Mark you the floore? that square & speckled stone,
    Which looks so firm and strong,
    Is Patience:
    George Herbert (1593–1633)

    Sprung from the West,
    He drank the valorous youth of a new world.
    The strength of virgin forests braced his mind,
    The hush of spacious prairies stilled his soul.
    His words were oaks in acorns; and his thoughts
    Were roots that firmly gript the granite truth.
    Edwin Markham (1852–1940)