Three points have been chosen randomly from the vertices of a n-sided regular polygon.

Determine the probability (in terms of n) that they form (a) an acute triangle; (b) a right triangle?

(In reply to re: computer findings for triangles through 50-gons by Charlie)

To repeat, it looks like the probability of a right triangle is zero for odd n and 3/(n-1) for even n.

... and it looks like for even n the probability of an acute triangle is (n/2 -2)/(n-1) and for odd n it's ((n-1)/2)/(n-2).

Posted by Charlie on 2011-08-14 17:21:57