A379469 Decimal expansion of (1 + sqrt(6))/(3*sqrt(2)).

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

Offset: 0

Author

Stefano Spezia, Dec 23 2024

Keywords

• nonn
• cons
• easy

Comments

This constant gives an upper bound to the Steiner ratio of a regular tetrahedron.

Examples

			0.81305252958514160597609690120357380207588039716628...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.6, p. 505.

Links

• Ding-Zhu Du and Warren D. Smith, Disproofs of Generalized Gilbert-Pollak Conjecture on the Steiner Ratio in Three or More Dimensions, Journal of Combinatorial Theory, Series A, Volume 74, Issue 1, 1996, Pages 115-130. See p. 128.
• Warren D. Smith, How to find Steiner minimal trees in euclidean d-space, Algorithmica 7, 137-177 (1992).

Crossrefs

Cf. A002193, A010464, A010474, A086180.

Programs

Mathematica

RealDigits[(1+Sqrt[6])/(3Sqrt[2]),10,100][[1]]

Formula

Equals A086180/A010474.

Minimal polynomial: 324*x^4 - 252*x^2 + 25. - Stefano Spezia, Aug 03 2025