Continued Fraction Expansion

Some articles on continued fraction expansion, continued fractions, continued fraction, fractions:

Transcendental Number - Properties
... 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 ...
Other Continued Fraction Expansions - Typical Continued Fractions
... 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 ...
Methods Of Computing Square Roots - Continued Fraction Expansion - Pell's Equation
... 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 ...

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