login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164102 Decimal expansion of 2*Pi^2. 13
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,2
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
REFERENCES
L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 15.
LINKS
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.
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
EXAMPLE
19.739208802178717237668981...
MATHEMATICA
RealDigits[2*Pi^2, 10, 120][[1]] (* Harvey P. Dale, Apr 19 2012 *)
PROG
(PARI) 2*Pi^2 \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
Sequence in context: A135449 A060388 A081821 * A105532 A111471 A078527
KEYWORD
cons,nonn,easy
AUTHOR
R. J. Mathar, Aug 10 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)