Reject pairs of independent uniform coordinates from the square until their squared radius lies in . Multiply each coordinate by to obtain two independent variables with the standard normal distribution. Squaring either gives a chi-squared variable with one degree of freedom.
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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.