Robert Hill (email@example.com) wrote: : In article <firstname.lastname@example.org>, email@example.com (Bill Taylor) writes: : : > Robert:- can you run off a few more million simulations using a 2D Cauchy; : > ====== and report back to us please? [snip] : In one million simulated triangles using the above method I got : : 283252 283206 283133 150409 : : where the first three figures are different ways of being obtuse and : the fourth is acute. I was very surprised by this.
With a Cauchy distribution large numbers [*] are much more likely than with a normal distribution, and so (I think) one is fairly likely to have one point much further from the origin than the other two; if two points are relatively close together and the other is much further away, then it's unlikely that the triangle will be acute, so I don't think the low probability of acuteness should be surprising.
[*] Large compared with the median absolute value, for example.