Continued Fractions & Rational Approximations
Continued fractions can be thought of as an alternative to digit sequences for representing numbers, based on division rather than multiplication by a base. Studied occasionally for at least half a millennium, continued fractions have become increasingly important through their applications to dynamical systems theory and number theoretic algorithms. Mathematica
has highly efficient original algorithms for finding large numbers of terms in continued fractions, as well as for handling exact continued fractions for quadratic irrationals.
continued fraction expansion
construct exact or inexact numbers from continued fractions
a list of successive convergents of a continued fraction
find rational approximations
test for a quadratic irrational (repeating continued fraction)