A374948 Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

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

Offset: 1

Author

Marco Ripà, Jul 24 2024

Keywords

• nonn
• cons
• easy

Comments

The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).

Also the surface area of a gyroelongated square pyramid (Johnson solid J_10) with unit edges. - Paolo Xausa, Aug 04 2025

Examples

			6.1961524227066318805823390245176171008284157614311418841674209383...
		

Links

• R. Bridges, Minimal Steiner Trees for Three Dimensional Networks, Math. Gaz., 78 (1994), 157-162.
• Math Overflow, Joining the 2^k points of {0,1}^k with the shortest tree.
• Mathematics Stack Exchange, Steiner tree problem in 3D.
• J. M. Smith, R. Weiss, and M. Patel, An O(N2) Heuristic for Steiner Minimal Trees in E3, Networks 26 (1995), 273-289.
• B. Toppur and J. M. A. Smith, A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space, J. Math. Modelling and Algorithms, 4 (2005), 199-217.
• Wikipedia, Gyroelongated square pyramid.

Crossrefs

Cf. A002194, A010482, A374148, A374260.

Essentially the same as A178809, A176532 and A010482.

Programs

Mathematica

RealDigits[3Sqrt[3]+1,10,87][[1]] (* Stefano Spezia, Jul 25 2024 *)

Formula

Equals 3*sqrt(3) + 1.

Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.