 Marsaglia polar method

Reject pairs of independent uniform coordinates from the square until their squared radius $S$ lies in $(0,1)$. Multiply each coordinate by $\sqrt{-2\log S/S}$ to obtain two independent variables with the standard normal distribution. Squaring either gives a chi-squared variable with one degree of freedom.

The Marsaglia polar method is an efficient algorithm for generating pairs of independent standard normally distributed random numbers (i.e., numbers that follow a normal distribution with a mean of 0 and a variance of 1). This method is especially notable because it avoids the use of trigonometric functions, making it computationally efficient.