A method for generating random numbers numbers with a Gaussian distribution (also known as a normal distribution) using numbers with a uniform distribution.

The basic form of the transformation starts with two uniformly distributed random numbers x_{1} and x_{2}. Then we can generate two normally distributed random numbers y_{1} and y_{2} as the following:

y_{1} = sqrt(-2ln(x_{1}))cos(2πx_{2})

y_{2} = sqrt(-2ln(x_{1}))sin(2πx_{2})

The new distribution has a mean of zero and a standard distribution of one.