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 \( \theta \in 2\pi [0,1] \).