Continued Fractions of Square Root

For a nonsquare positive integer $n$, its square root $\sqrt{n}$ can be represented in the form of infinite continued fractions: \[ \sqrt{n} = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{\ddots} } } } \] For convenience we use the notation $\sqrt{n}=[a_0;a_1,a_2,a_3,\ldots]$ for the continued fractions above. In addition, the continued fractions of $\sqrt{n}$ is periodic, i.e. $a_{k+T}=a_k$ where $T$ is the period and $k$ is any positive integer. So the continued fractions of $\sqrt{n}$ is likely written in the form \[ \sqrt{n} = [a_0; \overline{a_1,a_2,\ldots,a_T}] \] This calculator finds the continued fractions of $\sqrt{n}$ and returns the result in this form but with paranthesis instead of overline in the repeated parts.

Continued Fraction Calculator

Adblocker detected! Please consider reading this notice.

This website is made possible by displaying online advertisements to its visitors. Please consider supporting us by disabling your ad blocker.

Or add comnuan.com to your ad blocking whitelist.

×