## Quick Reference

An expression of the form *q*_{1}+1/*b*_{2}, where *b*_{2}=*q*_{2}+1/*b*_{3}, *b*_{3}=*q*_{3}+1/*b*_{4}, and so on, where *q*_{1}, *q*_{2},…are integers, usually positive. This can be written or, in a form that is easier to print,If the continued fraction terminates, it gives a rational number. The expression of any given positive rational number as a continued fraction can be found by using the Euclidean algorithm. For example, 1274/871 is found, by using the steps which appear in the entry on the Euclidean algorithm, to equalWhen the continued fraction continues indefinitely, it represents a real number that is the limit of the sequence For example, it can be shown thatis equal to the golden ratio, and that the representation of √2 as a continued fraction is

*Subjects:*
mathematics.