Some articles on continued fraction expansion, continued fractions, continued fraction, fractions:
... have unbounded partial quotients in its continued fraction expansion ... Using the explicit continued fraction expansion of e, one can show that e is not a Liouville number (although the partial quotients in its continued fraction expansion are unbounded) ... It is conjectured that all infinite continued fractions with bounded terms that are not eventually periodic are transcendental (eventually periodic continued fractions correspond to quadratic ...
... numbers do not have any periodic or regular behavior in their continued fraction expansion ... root of the denominator of the nth convergent of the continued fraction expansion of almost all real numbers approaches an asymptotic limit, which is known as Lévy's constant ... Lochs' theorem states that nth convergent of the continued fraction expansion of almost all real numbers determines the number to an average accuracy of just over n decimal places ...
... equation) and its variants yield a method for efficiently finding continued fraction convergents of square roots of integers ... (where p and q are integers) to the equation, then is a continued fraction convergent of, and as such, is an excellent rational approximation to it ... quickly, iterate Notice that the corresponding sequence of fractions coincides with the one given by the Hero's method starting with ...
Famous quotes containing the words expansion, continued and/or fraction:
“We are caught up Mr. Perry on a great wave whether we will or no, a great wave of expansion and progress. All these mechanical inventionstelephones, electricity, steel bridges, horseless vehiclesthey are all leading somewhere. Its up to us to be on the inside in the forefront of progress.”
—John Dos Passos (18961970)
“The cause of Sense, is the External Body, or Object, which presseth the organ proper to each Sense, either immediately, as in the Taste and Touch; or mediately, as in Seeing, Hearing, and Smelling: which pressure, by the mediation of Nerves, and other strings, and membranes of the body, continued inwards to the Brain, and Heart, causeth there a resistance, or counter- pressure, or endeavor of the heart, to deliver it self: which endeavor because Outward, seemeth to be some matter without.”
—Thomas Hobbes (15791688)
“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)