How to generate random points in a circular distribution

Question

I am wondering how i could generate random numbers that appear in a circular distribution.

I am able to generate random points in a rectangular distribution such that

Answer 1

I would use polar coordinates:

r_squared, theta = [random.randint(0,250000), 2*math.pi*random.random()]

Then r is always less than or equal to the radius, and theta always between 0 and 2*pi radians.

Since r is not at the origin, you will always convert it to a vector centered at 500, 500, if I understand correctly

x = 500 + math.sqrt(r_squared)*math.cos(theta) y = 500 + math.sqrt(r_squared)*math.sin(theta)

Choose r_squared randomly because of this