A088367 Decimal expansion of Krivine's bound for Grothendieck's constant, Pi/(2*log(1+sqrt(2))).

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

Offset

1,2

Comments

Krivine (1977) proved that Grothendieck's constant <= Pi/(2*log(1+sqrt(2))), and conjectured that this bound is the exact value of the constant. His conjecture was refuted by Braverman et al. (2013). - Amiram Eldar, Jun 24 2021

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 3.11, pp. 235-237.

Links

G. C. Greubel, Table of n, a(n) for n = 1..20000

Noga Alon, Konstantin Makarychev, Yury Makarychev and Assaf Naor, Quadratic forms on graphs, Inventiones Math., Vol. 163 (2006), pp. 499-522; preprint.

Mark Braverman, Konstantin Makarychev, Yury Makarychev and Assaf Naor, The Grothendieck constant is strictly smaller than Krivine's bound, Forum of Mathematics, Pi, Vol. 1 (2013), e4.

Jean-Louis Krivine, Sur la constante de Grothendieck, C. R. Acad. Sci. Paris, Series A and B, Vol. 284, No. 8 (1977), pp. A445-A446.

Simon Plouffe, Grothendieck's majorant.

Eric Weisstein's World of Mathematics, Grothendieck's Constant.

Wikipedia, Grothendieck inequality.

Example

1.7822139781913691117744134529725493407917319097732...

Mathematica

RealDigits[Pi/(2*Log[1 + Sqrt[2]]), 10, 111][[1]] (* Robert G. Wilson v, May 19 2004 *)

Prog

(PARI) Pi/(2*log(1 + sqrt(2))) \\ G. C. Greubel, Mar 27 2018
(Magma) SetDefaultRealField(RealField(150)); R:= RealField(); Pi(R)/(2*Log(1 + Sqrt(2))) // G. C. Greubel, Mar 27 2018

Crossrefs

Sequence in context: A154169 A245260 A128755 * A196610 A198938 A244067

Adjacent sequences: A088364 A088365 A088366 * A088368 A088369 A088370

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 27 2003

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

Named edited by Amiram Eldar, Jun 24 2021

Status

approved