A176532 -id:A176532 - cp's OEIS frontend

A178809 Decimal expansion of the area of the regular 12-gon (dodecagon) of edge length 1.

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

Offset: 2

Vladimir Joseph Stephan Orlovsky, Jun 16 2010

Surface area of a regular hexagonal prism with unit side length and height. - Wesley Ivan Hurt, May 04 2021

			11.196152422706631880582339024517617100828415761431141884167420938355...

G. C. Greubel, Table of n, a(n) for n = 2..10000
Index entries for algebraic numbers, degree 2

Cf. A010482, A090488, A104956, A120011, A176532.

Mathematica
```
RealDigits[N[6+3*Sqrt[3],150]][[1]]
```

sqrt(27)+6 \\ Charles R Greathouse IV, Apr 25 2016

Equals 6+3*sqrt(3).

Equals 1 + A176532 = 6 + A010482. - R. J. Mathar, Jun 25 2010

Offset corrected and keyword:cons inserted by R. J. Mathar, Jun 25 2010

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

Original entry on oeis.org

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

Marco Ripà, Jul 24 2024

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

			6.1961524227066318805823390245176171008284157614311418841674209383...

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.

Cf. A002194, A010482, A374148, A374260.

Essentially the same as A178809, A176532 and A010482.

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

Equals 3*sqrt(3) + 1.

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

cp's OEIS Frontend

A178809 Decimal expansion of the area of the regular 12-gon (dodecagon) of edge length 1.

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