The square roots of all (positive) integers that are not perfect squares are quadratic irrationals, and hence are unique periodic continued fractions.
* The successive approximations generated in finding the continued fraction representation of a number, that is, by truncating the continued fraction representation, are in a certain sense (described below) the "best possible".

Formulation

A continued fraction in canonical form is an expression of the form

where a_i are integer numbers, called the coefficients

1.Previous
3.Next