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)

    “Rationalists, wearing square hats,
    Think, in square rooms,
    Looking at the floor,
    Looking at the ceiling.
    They confine themselves
    To right-angled triangles.”
    —Wallace Stevens (1879–1955)

    ““Jim,” she said earnestly, “if I was put down there in the middle of the night, I could find my way all over that little town; and along the river to the next town, where my grandmother lived. My feet remember all the little paths through the woods, and where the big roots stick out to trip you. I ain’t never forgot my own country.””
    —Willa Cather (1873–1947)