Maeckes logo

<    1      2    >


Continued fraction for the square root

The continued fraction for the square root is

 


Explanation

The identity for the square root is

In the right-hand section you can substitute x and this will immediately result in the continued fraction

 


Example 1

The successive convergences of 2 give

and that's pretty close to the value 1.414213562… your calculator shows.

 


History

In 1579, the Italian mathematician Rafael Bombelli used continued fractions to calculate square roots.


Deutsch   Español   Français   Nederlands   中文   Русский