 TOPICS  # Gaussian Triangle Picking

Finch (2010) gives an overview of known results for random Gaussian triangles.

Let the vertices of a triangle in dimensions be normal (normal) variates. The probability that a Gaussian triangle in dimensions is obtuse is   (1)   (2)   (3)   (4)   (5)

where is the gamma function, is the hypergeometric function, and is an incomplete beta function.

For even , (6)

(Eisenberg and Sullivan 1996).

The first few cases are explicitly   (7)   (8)   (9)   (10)

(OEIS A102519 and A102520). The even cases are therefore 3/4, 15/32, 159/512, 867/4096, ... (OEIS A102556 and A102557) and the odd cases are , where , 9/8, 27/20, 837/560, ... (OEIS A102558 and A102559).

Disk Triangle Picking

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## References

Eisenberg, B. and Sullivan, R. "Random Triangles Dimensions." Amer. Math. Monthly 103, 308-318, 1996.Finch, S. "Random Triangles." http://algo.inria.fr/csolve/rtg.pdf. Jan. 21, 2010.Sloane, N. J. A. Sequences A102519, A102520, A102556, A102557, A102558, and A102559 in "The On-Line Encyclopedia of Integer Sequences."

## Referenced on Wolfram|Alpha

Gaussian Triangle Picking

## Cite this as:

Weisstein, Eric W. "Gaussian Triangle Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussianTrianglePicking.html