A088367 - OEIS

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

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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