A394175 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.

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, 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, 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

Offset

0,3

Links

Table of n, a(n) for n=0..105.

Dominik Beck, On Random Simplex Picking Beyond the Blashke Problem, arXiv:2412.07952 [math.MG], 2024.

Dominik Beck, Random polytopes, doctoral thesis, Mathematical Institute of Charles University, Prague, 2025.

Eric Weisstein's World of Mathematics, Triangular Prism.

Wikipedia, Triangular prism.

Index entries for transcendental numbers.

Formula

Equals 1859/116640 - Pi^2/17010.

Example

0.0153577050126735630833528615912281314245357417554042...

Mathematica

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

Prog

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

Crossrefs

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).

Sequence in context: A269893 A336055 A131925 * A128010 A185046 A114740

Adjacent sequences: A394172 A394173 A394174 * A394176 A394177 A394178

Keyword

nonn,cons

Author

Amiram Eldar, Mar 11 2026

Status

approved