The Expected Volume of a Tetrahedron whose Vertices are Chosen at Random in the Interior of a Cube |
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| Authors: | Alessandro Zinani |
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| Affiliation: | (1) Parma, Italy, IT |
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| Abstract: |  We calculate E[V 4(C)], the expected volume of a tetrahedron whose vertices are chosen randomly (i.e. independently and uniformly) in the interior of C, a cube of unit volume. We find The result is in convincing agreement with a simulation of 3000 ·106 trials.Received February 12, 2002; in revised form August 13, 2002Published online February 28, 2003 |
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| Keywords: | 2000 Mathematics Subject Classification: 60D05 |
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![$$E[V_4 {rm (cube)}]={3977over 216000} - {pi^2 over 2160}=0.01384277574ldots$$](/content/l4bbjm0yayytw5v8/605_2002_Article_531_TeX2GIFEqu1.gif)