A088367 - OEIS

%I #24 Feb 16 2025 08:32:51

%S 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,

%T 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,

%U 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

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

%C 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

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

%H G. C. Greubel, <a href="/A088367/b088367.txt">Table of n, a(n) for n = 1..20000</a>

%H Noga Alon, Konstantin Makarychev, Yury Makarychev and Assaf Naor, <a href="https://doi.org/10.1007/s00222-005-0465-9">Quadratic forms on graphs</a>, Inventiones Math., Vol. 163 (2006), pp. 499-522; <a href="http://konstantin.makarychev.net/pdf/qforms.pdf">preprint</a>.

%H Mark Braverman, Konstantin Makarychev, Yury Makarychev and Assaf Naor, <a href="https://doi.org/10.1017/fmp.2013.4">The Grothendieck constant is strictly smaller than Krivine's bound</a>, Forum of Mathematics, Pi, Vol. 1 (2013), e4.

%H Jean-Louis Krivine, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k57974407/f31.item">Sur la constante de Grothendieck</a>, C. R. Acad. Sci. Paris, Series A and B, Vol. 284, No. 8 (1977), pp. A445-A446.

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap48.html">Grothendieck's majorant</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GrothendiecksConstant.html">Grothendieck's Constant</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Grothendieck_inequality">Grothendieck inequality</a>.

%e 1.7822139781913691117744134529725493407917319097732...

%t RealDigits[Pi/(2*Log[1 + Sqrt[2]]), 10, 111][[1]] (* _Robert G. Wilson v_, May 19 2004 *)

%o (PARI) Pi/(2*log(1 + sqrt(2))) \\ _G. C. Greubel_, Mar 27 2018

%o (Magma) SetDefaultRealField(RealField(150)); R:= RealField(); Pi(R)/(2*Log(1 + Sqrt(2))) // _G. C. Greubel_, Mar 27 2018

%K nonn,cons,changed

%O 1,2

%A _Eric W. Weisstein_, Sep 27 2003

%E Edited by _N. J. A. Sloane_, Oct 01 2006

%E Named edited by _Amiram Eldar_, Jun 24 2021