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 mannerin 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 (16721719)
“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 (18601935)
“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 (16231662)
“A good word is as a good tree
its roots are firm,
and its branches are in heaven;
it gives its produce every season
by the leave of its Lord.”
—QurAn. Abraham 14:29-30, ed. Arthur J. Arberry (1955)