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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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Some Thoughts Research | Comment 8 of 12 |
From the simulations ran be Charlie and Steven we have two data points for a more general problem of picking an acute triangle in an n-dimensional ball.

These do agree with the values I found at http://mathworld.wolfram.com/BallTrianglePicking.html which gives exact values.
               Simulation  Exact
2D probability 0.2794364  0.280285 = 4/pi^2 - 1/8
3D probability 0.4713054  0.471429 = 33/70

  Posted by Brian Smith on 2018-12-25 13:54:30
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