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A127454
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Decimal expansion of transcendental solution to round pegs in square holes problem.
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2
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8, 1, 3, 7, 9, 4, 1, 0, 4, 6, 0, 9, 1, 3, 7, 2, 3, 7, 6, 5, 2, 9, 8, 3, 8, 9, 8, 4, 0, 5, 3, 2, 2, 3, 3, 7, 0, 0, 9, 6, 7, 2, 5, 3, 0, 9, 7, 6, 2, 4, 4, 3, 7, 6, 9, 5, 8, 3, 5, 3, 0, 9, 9, 2, 2, 4, 6, 3, 0, 9, 4, 1, 2, 0, 5, 6, 6, 0, 1, 6, 0, 7, 7, 8, 7, 7, 6, 4, 2, 8, 6, 6, 5, 9, 8, 8, 9, 8, 1, 8, 8, 1, 3, 6, 5
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OFFSET
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1,1
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COMMENTS
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This value "must be determined numerically. As a result, a round peg fits better into a square hole than a square peg fits into a round hole only for integer dimensions n < 9."
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LINKS
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Eric Weisstein's World of Mathematics, Peg.
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FORMULA
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Where the real number ratio crosses 1 in (Pi^n)(n^(n/2))/(2^(2n))(Gamma(1+n/2))^2. n such that (Pi^n)(n^(n/2)) = (2^(2n))(Gamma(1+n/2))^2.
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EXAMPLE
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8.13794104609137237652983898405322337009672530976244376958353099224630941205660...
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MATHEMATICA
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RealDigits[ FindRoot[ Pi^x*x^(x/2) == 2^(2 x) Gamma[1 + x/2]^2, {x, 8}, WorkingPrecision -> 121][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Jul 03 2014 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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