We give an elementary geometric proof using Ford circles of a well-known theorem of Lagrange, which says that the convergents of the continued fraction expansion of a real number α coincide with the rationals that are best approximations of α
AbstractIn the study of simultaneous rational approximation of functions using rational functions wi...
Given a real number α, we aim at computing the best rational approximation with at most k digits and...
The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fract...
Fundamental to the theory of continued fractions is the fact that every infinite continued fraction ...
There are numerous methods for rational approximation of real numbers. Continued fraction convergent...
While the traditional form of continued fractions is well-documented, a new form, designed to approx...
AbstractA new continued fraction algorithm is given and analyzed. It yields approximations for an ir...
Includes bibliographical references (pages 63-64)Following is my thesis submitted in partial satisfa...
The best rational approximation of a real number are rational numbers that are closest to the real n...
Rational approximations to real numbers have been used from ancient times, either for convenience in...
Continued fractions offer a concrete representation of arbitrary real numbers, where in the past suc...
In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, a...
AbstractWe investigate a one-parameter family of infinite generalised continued fractions. The fract...
summary:Let $\xi=[a_0;a_1,a_2,\dots,a_i,\dots]$ be an irrational number in simple continued fraction...
Inspired by work of Ford, we describe a geometric representation of real and complex continued fract...
AbstractIn the study of simultaneous rational approximation of functions using rational functions wi...
Given a real number α, we aim at computing the best rational approximation with at most k digits and...
The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fract...
Fundamental to the theory of continued fractions is the fact that every infinite continued fraction ...
There are numerous methods for rational approximation of real numbers. Continued fraction convergent...
While the traditional form of continued fractions is well-documented, a new form, designed to approx...
AbstractA new continued fraction algorithm is given and analyzed. It yields approximations for an ir...
Includes bibliographical references (pages 63-64)Following is my thesis submitted in partial satisfa...
The best rational approximation of a real number are rational numbers that are closest to the real n...
Rational approximations to real numbers have been used from ancient times, either for convenience in...
Continued fractions offer a concrete representation of arbitrary real numbers, where in the past suc...
In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, a...
AbstractWe investigate a one-parameter family of infinite generalised continued fractions. The fract...
summary:Let $\xi=[a_0;a_1,a_2,\dots,a_i,\dots]$ be an irrational number in simple continued fraction...
Inspired by work of Ford, we describe a geometric representation of real and complex continued fract...
AbstractIn the study of simultaneous rational approximation of functions using rational functions wi...
Given a real number α, we aim at computing the best rational approximation with at most k digits and...
The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fract...
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