A394176 Decimal expansion of the mean volume of a tetrahedron whose vertices are uniformly and independently selected at random in the interior of a square pyramid of unit volume.

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

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, Square Pyramid.

Wikipedia, Square pyramid.

Index entries for transcendental numbers.

Formula

Equals 941*Pi^2/72072 - 977/8640.

Example

0.0157826813199543945913797688082767910561224582206716...

Mathematica

RealDigits[941*Pi^2/72072 - 977/8640, 10, 120, -1][[1]]

Prog

(PARI) 941*Pi^2/72072 - 977/8640

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), A394175 (triangular prism), this constant (square pyramid).

Sequence in context: A063006 A135096 A153104 * A233527 A244355 A374771

Adjacent sequences: A394173 A394174 A394175 * A394177 A394178 A394179

Keyword

nonn,cons

Author

Amiram Eldar, Mar 11 2026

Status

approved