Comment by tzs
19 days ago
Maybe it should be the cube of the amount of circumference inside the unit circle, because 3 random points have to land on the circle for it to be chosen.
19 days ago
Maybe it should be the cube of the amount of circumference inside the unit circle, because 3 random points have to land on the circle for it to be chosen.
I think that's correct.
But that wouldn't work either. The problem is that there is an infinite volume of circles with ~2 as the circumference inside the unit circle. (Volume in x,y,r space, and, consequently in the proposed probability distribution as well.) So this proposed probability distribution gives infinity, when summed up.