All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Triangular Polygons (Posted on 2011-08-12)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: computer findings for triangles through 50-gons | Comment 2 of 4 |
(In reply to computer findings for triangles through 50-gons by Charlie)

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

In reduced proper fractions, all the numbers given before are:

4  0  1
5  2//3  0
6  1//5  3//5
7  3//5  0
8  2//7  3//7
9  4//7  0
10  1//3  1//3
11  5//9  0
12  4//11  3//11
13  6//11  0
14  5//13  3//13
15  7//13  0
16  2//5  1//5
17  8//15  0
18  7//17  3//17
19  9//17  0
20  8//19  3//19
21  10//19  0
22  3//7  1//7
23  11//21  0
24  10//23  3//23
25  12//23  0
26  11//25  3//25
27  13//25  0
28  4//9  1//9
29  14//27  0
30  13//29  3//29
31  15//29  0
32  14//31  3//31
33  16//31  0
34  5//11  1//11
35  17//33  0
36  16//35  3//35
37  18//35  0
38  17//37  3//37
39  19//37  0
40  6//13  1//13
41  20//39  0
42  19//41  3//41
43  21//41  0
44  20//43  3//43
45  22//43  0
46  7//15  1//15
47  23//45  0
48  22//47  3//47
49  24//47  0
50  23//49  3//49

The double slashes are an artifact of UBASIC's processing.

Edited on August 14, 2011, 5:10 pm
 Posted by Charlie on 2011-08-14 17:08:52

 Search: Search body:
Forums (0)