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A358614
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Decimal expansion of 9*sqrt(2)/32.
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0
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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Smallest constant M such that the inequality
|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
holds for all real numbers a, b, 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.
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).
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).
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LINKS
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The IMO compendium, Problem 3, 47th IMO 2006.
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FORMULA
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EXAMPLE
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0.3977475644174329824...
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MAPLE
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evalf(9*sqrt(2)/32), 100);
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MATHEMATICA
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RealDigits[9*Sqrt[2]/32, 10, 120][[1]] (* Amiram Eldar, Dec 05 2022 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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