Given "u" and "v", independent and uniformly distributed in the closed interval [−1, +1], set . If or , discard "u" and "v", and try another pair ("u", "v"). Because "u" and "v" are uniformly distributed and because only points within the unit circle have been admitted, the values of "s" will be uniformly distributed in the open interval (0, 1), too. The latter can be seen by calculating the cumulative distribution function for "s" in the interval (0, 1). This is the area of a circle with radius formula_5, divided by formula_6. From this we find the probability density function to have the constant value 1 on the interval (0, 1). Equally so, the angle θ divided by formula_7 is uniformly distributed in the interval [0, 1) and independent of "s".