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%I #52 Dec 17 2022 20:02:05
%S 3,9,7,7,4,7,5,6,4,4,1,7,4,3,2,9,8,2,4,7,5,4,7,4,9,5,3,6,8,3,9,7,7,5,
%T 8,4,5,9,7,7,2,0,2,1,4,9,4,9,7,6,6,6,4,5,5,8,0,9,4,1,1,7,6,3,0,9,8,9,
%U 3,5,0,9,5,6,7,4,6,7,6,0,4,6,7,6,6,7,1,4,9,4,0,2,9,6,4,9,1,9,2
%N Decimal expansion of 9*sqrt(2)/32.
%C Smallest constant M such that the inequality
%C |a*b*(a^2 - b^2) + b*c*(b^2 - c^2) + c*a*(c^2 - a^2)| <= M * (a^2 + b^2 + c^2)^2
%C holds for all real numbers a, b, c.
%C Equality stands for any triple (a, b, c) proportional to (1 - 3*sqrt(2)/2, 1, 1 + 3*sqrt(2)/2), up to permutation.
%C This constant is the answer to the 3rd problem, proposed by Ireland during the 47th International Mathematical Olympiad in 2006 at Ljubljana, Slovenia (see links).
%C Equivalently |(a - b)(b - c)(c - a)(a + b + c)| / (a^2 + b^2 + c^2)^2 <= M with (a,b,c) != (0,0,0).
%H Evan Chen, <a href="https://web.evanchen.cc/exams/IMO-2006-notes.pdf">IMO 2006/3</a>, IMO 2006 Solution Notes.
%H The IMO compendium, <a href="https://imomath.com/othercomp/I/Imo2006.pdf">Problem 3</a>, 47th IMO 2006.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F Equals (3/16) * A230981 = (3/32) * A010474 = (9/32) * A002193 = (9/16) * A010503.
%e 0.3977475644174329824...
%p evalf(9*sqrt(2)/32), 100);
%t RealDigits[9*Sqrt[2]/32, 10, 120][[1]] (* _Amiram Eldar_, Dec 05 2022 *)
%Y Cf. A002193, A010474, A010503, A230981.
%K nonn,cons,easy
%O 0,1
%A _Bernard Schott_, Dec 05 2022
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