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Triangular Polygons II (Posted on 2011-10-11) 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 the center of the given polygon lies in the interior of the triangle determined by the three chosen points.

No Solution Yet Submitted by K Sengupta    
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Solution table Comment 2 of 2 |
(In reply to solution by Charlie)

 n

 3 1.0000000000
 4                0.0000000000
 5 0.5000000000
 6                0.1000000000
 7 0.4000000000
 8                0.1428571429
 9 0.3571428571
10                0.1666666667
11 0.3333333333
12                0.1818181818
13 0.3181818182
14                0.1923076923
15 0.3076923077
16                0.2000000000
17 0.3000000000
18                0.2058823529
19 0.2941176471
20                0.2105263158
21 0.2894736842
22                0.2142857143
23 0.2857142857
24                0.2173913043
25 0.2826086957
26                0.2200000000
27 0.2800000000
28                0.2222222222
29 0.2777777778
30                0.2241379310
31 0.2758620690
32                0.2258064516
33 0.2741935484
34                0.2272727273
35 0.2727272727
36                0.2285714286
37 0.2714285714
38                0.2297297297
39 0.2702702703
40                0.2307692308
41 0.2692307692
42                0.2317073171
43 0.2682926829
44                0.2325581395
45 0.2674418605
46                0.2333333333
47 0.2666666667
48                0.2340425532
49 0.2659574468
50                0.2346938776

  Posted by Charlie on 2011-10-11 15:27:06
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