A394175 - OEIS

%I #7 Mar 11 2026 15:06:22

%S 0,1,5,3,5,7,7,0,5,0,1,2,6,7,3,5,6,3,0,8,3,3,5,2,8,6,1,5,9,1,2,2,8,1,

%T 3,1,4,2,4,5,3,5,7,4,1,7,5,5,4,0,4,2,2,5,5,1,6,7,6,9,7,4,2,3,4,5,1,1,

%U 7,3,7,9,2,9,7,1,3,3,8,8,9,5,6,0,4,7,4,1,2,6,5,8,8,0,6,2,7,9,3,3,2,3,6,2,3,9

%N Decimal expansion of the mean volume of a tetrahedron whose vertices are uniformly and independently selected at random in the interior of a triangular prism of unit volume.

%H Dominik Beck, <a href="https://arxiv.org/abs/2412.07952">On Random Simplex Picking Beyond the Blashke Problem</a>, arXiv:2412.07952 [math.MG], 2024.

%H Dominik Beck, <a href="https://www2.karlin.mff.cuni.cz/~beckd/lectures/DISSERTATION.pdf">Random polytopes</a>, doctoral thesis, Mathematical Institute of Charles University, Prague, 2025.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularPrism.html">Triangular Prism</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Triangular_prism">Triangular prism</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals 1859/116640 - Pi^2/17010.

%e 0.0153577050126735630833528615912281314245357417554042...

%t RealDigits[1859/116640 - Pi^2/17010, 10, 120, -1][[1]]

%o (PARI) 1859/116640 - Pi^2/17010

%Y Tetrahedron volume in: A093524 (cube), A093525 (tetrahedron), A093591 (ball), A394169 (surface of sphere), A394170 (octahedron), A394171 (rhombic dodecahedron), A394172 (cuboctahedron), A394173 (truncated tetrahedron), A394174 (triangular bipyramid), this constant (triangular prism), A394176 (square pyramid).

%K nonn,cons

%O 0,3

%A _Amiram Eldar_, Mar 11 2026