Sequence of Best Rational Approximations to Square Root of 2/Historical Note

Historical Note on Sequence of Best Rational Approximations to Square Root of 2
The sequence of best rational approximations to the square root of $2$ was known to in the $2$nd century C.E.

More precisely, he knew that if $\dfrac p q$ is an approximation to $\sqrt 2$, then $\dfrac {p + 2 q} {p + q}$ is a better one, which result is demonstrated in Relation between Adjacent Best Rational Approximations to Root 2.