I have seen a result about the approximation of irrational numbers and want to find its proof.
Suppose $\alpha$ is an irrational number, then there are infinitely many integers $p,q$ with $(p,q)=1$ such that $$\left|\alpha -\frac{p}{q}\right| \le \frac{1}{\sqrt{5}q^2}.$$
Is there a name attached to this theorem? Where can I find the proof of it?
Thanks in advance!