continued fraction

He made contributions to the theory of continued fractions.

His work included the development of continued fractions and a method for their representation.

To illustrate the use of generalized continued fractions, consider the following example.

If a real number r is written as a simple continued fraction:

This problem was solved during the 18th century by means of continued fractions.

It is used to show the repeating terms in a periodic continued fraction.

It is sometimes necessary to separate a continued fraction into its even and odd parts.

Another meaning for generalized continued fraction is a generalization to higher dimensions.

Unfortunately, this particular continued fraction does not converge to a finite number in every case.

Rational numbers have two continued fractions; the version in this list is the shorter one.