A164102 Decimal expansion of 2*Pi^2.

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

Offset: 2

Author

R. J. Mathar, Aug 10 2009

Keywords

• cons
• nonn
• easy

Comments

Surface area of the 4-dimensional unit sphere. The volume of the 4-dimensional unit sphere is a fourth of this, A102753.

Also decimal expansion of Pi^2/5 = 1.973920..., with offset 1. - Omar E. Pol, Oct 04 2011

Examples

			19.739208802178717237668981...
		

References

• L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 15.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..5000
• Yann Bernard, Autour des surfaces de Willmore, Images des Mathématiques, CNRS, 2014 (in French).
• Fernando C. Marques and André Neves, Min-Max theory and the Willmore conjecture, arXiv:1202.6036 [math.DG], 2012-2013.
• H.-J. Seiffert, Problem B-705, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 29, No. 4 (1991), p. 372; An Application of a Series Expansion for (arcsinx)^2, Solution to Problem B-705, ibid., Vol. 31, No. 1 (1993), pp. 85-86.
• Eric Weisstein's World of Mathematics, Hypersphere.
• Wikipedia, Hypersphere.
• Wikipedia, Willmore conjecture.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000032, A002388, A002736, A005248, A091476, A013661.

Programs

Mathematica

RealDigits[2*Pi^2,10,120][[1]] (* Harvey P. Dale, Apr 19 2012 *)

PARI

2*Pi^2 \\ Charles R Greathouse IV, Jan 24 2014

Formula

Equals 2*A002388 = 4*A102753.

Pi^2/5 = Sum_{k>=1} Lucas(2*k)/(k^2*binomial(2*k,k)) = Sum_{k>=1} A005248(k)/A002736(k) (Seiffert, 1991). - Amiram Eldar, Jan 17 2022