With $$\begin{equation*} x=r\cos{(\theta)}=\sqrt{2u}\cos{(\theta)}, \end{equation*}$$ and $$\begin{equation*} y=r\sin{(\theta)}=\sqrt{2u}\sin{(\theta)}, \end{equation*}$$ we can obtain new random numbers $x,y$ through $$\begin{equation*} x=\sqrt{-2\ln{(1-x')}}\cos{(\theta)}, \end{equation*}$$ and $$\begin{equation*} y=\sqrt{-2\ln{(1-x')}}\sin{(\theta)}, \end{equation*}$$ with $x'\in [0,1]$ and $\theta \in 2\pi [0,1]$.