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Triangular Polygons (Posted on 2011-08-12) Difficulty: 3 of 5
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?

See The Solution Submitted by K Sengupta    
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Solution re(2): computer findings for triangles through 50-gons | Comment 3 of 4 |
(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
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