History
This idea dates back to Laplace, whom Gauss credits with finding the above
by taking the square root of
The transformation to polar coordinates makes evident that θ is uniformly distributed (constant density) from 0 to 2π, and that the radial distance r has density
(Note that r2 has the appropriate chi square distribution.)
This method of producing a pair of independent standard normal variates by radially projecting a random point on the unit circumference to a distance given by the square root of a chi-square-2 variate is called the polar method for generating a pair of normal random variables,
Read more about this topic: Marsaglia Polar Method
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