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Probably Acute (Posted on 2018-12-21) Difficulty: 4 of 5
Three points are randomly selected inside a sphere.

What is the probability that the three points form an acute angled triangle?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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re: Not one answer | Comment 4 of 12 |
(In reply to Not one answer by broll)

All the articles referenced point out the difficulties in getting uniformly distributed points (points selected from a uniform distribution, where no point or region has a higher likelihood than any other region of the same size). That is presumably the ideal, and any such selection criterion will produce the same result. As at least one of the articles points out, the selection method used in my simulation, while fulfilling the criterion, is wasteful, in rejecting a large number of points as those chosen within the circumscribed cube but falling outside the sphere need to be replaced.  The articles describe ways of, say, making some portion of the criteria non-uniform (such as distance from center, latitude, longitude) to overcome the spatial non-uniformity of point selection without creating unusable points.

But if uniformity of point selection is kept, any method that produces such a uniform distribution would find the same result, even as the case of defining such uniformity in dV in a calculus method of finding the result.

  Posted by Charlie on 2018-12-22 08:34:36
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