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