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A337402
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Decimal expansion of the length of third shortest diagonal in a regular 12-gon with unit edge length.
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2
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3, 3, 4, 6, 0, 6, 5, 2, 1, 4, 9, 5, 1, 2, 3, 1, 6, 2, 2, 3, 0, 1, 1, 7, 5, 1, 2, 3, 6, 6, 7, 4, 9, 2, 8, 1, 3, 8, 3, 7, 4, 8, 1, 5, 5, 3, 3, 9, 3, 7, 5, 7, 1, 7, 3, 9, 8, 1, 3, 6, 5, 8, 9, 0, 6, 1, 1, 5, 7, 8, 9, 0, 6, 4, 2, 1, 8, 1, 8, 0, 7, 1, 5, 4, 5, 5, 1
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OFFSET
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1,1
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COMMENTS
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The distinct diagonal lengths in a regular 12-gon ABC...JKL with unit edge length are
AC = sqrt(2 + sqrt(3)) = sqrt(2)/(-1+sqrt(3)) = A188887
AD = sqrt(4 + 2*sqrt(3)) = 2 /(-1+sqrt(3)) = A090388
AE = sqrt(6 + 3*sqrt(3)) = sqrt(6)/(-1+sqrt(3))
AF = sqrt(7 + 4*sqrt(3)) = (1+sqrt(3))/(-1+sqrt(3)) = A019973
AG = sqrt(8 + 4*sqrt(3)) = 2*sqrt(2)/(-1+sqrt(3)) = A214726
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LINKS
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FORMULA
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Equals sin(Pi/3)/sin(Pi/12) = sqrt(2) + 2*cos(Pi/12) = sqrt(3*cot(Pi/12)).
Equals sqrt(6 + 3*sqrt(3)) = sqrt(6)/(-1+sqrt(3)) = (3+sqrt(3))/sqrt(2).
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EXAMPLE
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3.34606521495123162230117512366749281383748155339375...
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MATHEMATICA
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First[RealDigits[Sqrt[6+3Sqrt[3]], 10, 100]] (* Paolo Xausa, Oct 19 2023 *)
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PROG
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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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