A366019 Decimal expansion of the average distance between two points in a regular tetrahedron of unit volume.

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

Offset

0,1

Links

Table of n, a(n) for n=0..84.

Dominik Beck, Mean distance in polyhedra, arXiv:2309.13177 [math.PR], 22 Sep 2023.

Eric Weisstein's World of Mathematics, Tetrahedron Line Picking.

Formula

Equals 3^(1/3)*(sqrt(2)/7 - 37*Pi/315 + (4/15)*arctan(sqrt(2)) + 113*log(3)/(210*sqrt(2))) (Beck, 2023). - Amiram Eldar, May 15 2026

Example

0.72946242448431865807023909122203062872917613568627...

Mathematica

RealDigits[3^(1/3) (Sqrt[2]/7 - 37 Pi/315 + 4/15 ArcTan[Sqrt[2]] + 113 Log[3]/(210 Sqrt[2])), 10, 85][[1]]

Prog

(PARI) 3^(1/3)*(sqrt(2)/7 - 37*Pi/315 + (4/15)*atan(sqrt(2)) + 113*log(3)/(210*sqrt(2))) \\ Amiram Eldar, May 15 2026

Crossrefs

Cf. A073012.

Analogous constants: A073012 (cube), this constant (regular tetrahedron), A394103 (regular octahedron), A394104 (regular icosahedron), A394105 (regular dodecahedron).

Sequence in context: A092036 A021987 A031026 * A216186 A333360 A021936

Adjacent sequences: A366016 A366017 A366018 * A366020 A366021 A366022

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 26 2023

Extensions

Offset corrected by Amiram Eldar, May 15 2026

Status

approved