alt Hacker NewsIt's improperly formed as a question - the ruffian can shoot whenever he likes;
Consider:
Does "random" mean
1. uniform distribution on x and y coordinates with some sort of capping at the circle boundary? Or perhaps uniform across all possible x,y pairs inside (on the edge also?) of the circle? what about a normal distribution?
2. a choice of an angle and a length?
3. A point using 1 or 2, and then a random walk for 2 and 3?
I could go on. The worked solution is for random = uniform distribution across all possible reals inside the boundary, I think.
Replies
The article currently says
> Three points are chosen independently and uniformly at random from the interior of a unit circle
Has it been edited in the last 15 minutes to address your objection or something?
Author here: when calculating this I _did_ assume a uniform (area) distribution on the unit disk.
Now it does say
> Three points are chosen independently and uniformly at random from the interior of a unit circle.
which sounded OK to me at the time but I understand there could have been some ambiguity. Especially around the "uniform on area" part.
Also, I think that with rejection sampling you could get the same with 1) [0], 2) would work (provided correct scaling) [1]. No idea about 3) or the normal distribution thing you mentioned - I figured the problem was hairy enough already!
[0] https://blog.szczepan.org/blog/monte-carlo/#sampling-uniform... [1] https://blog.szczepan.org/blog/monte-carlo/