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A227472
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Decimal expansion of the side of the equilateral triangle that can cover every triangle of perimeter 2.
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1
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1, 0, 0, 2, 8, 5, 1, 4, 2, 6, 6, 3, 4, 1, 8, 0, 6, 6, 3, 0, 4, 0, 6, 1, 3, 9, 9, 7, 6, 4, 5, 5, 0, 3, 0, 3, 3, 1, 0, 4, 9, 7, 8, 6, 3, 1, 2, 3, 9, 0, 3, 2, 3, 1, 4, 0, 0, 3, 5, 0, 1, 2, 1, 6, 3, 0, 3, 4, 6, 7, 6, 7, 1, 8, 1, 4, 5, 2, 8, 5, 5, 3, 3, 4, 2, 3, 5, 2, 5, 0, 3, 4, 7, 3, 7, 8, 6, 0, 1, 3
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OFFSET
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1,4
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COMMENTS
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Curiously, this side is not 1, as intuitively expected, but a little greater than 1.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 494.
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LINKS
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FORMULA
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2/f(x0) where x0 is the global minimum of the trigonometric function f(x) = sqrt(3)*(1+sin(x/2))*sec(Pi/6-x) on the interval [0, Pi/6].
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EXAMPLE
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1.00285142663418066304061399764550303310497863123903231400350121630346767...
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MATHEMATICA
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f[x_] := Sqrt[3]*(1 + Sin[x/2])*Sec[Pi/6 - x]; x0 = x /. ToRules @ Reduce[0 < x < Pi/6 && f'[x] == 0, x, Reals]; RealDigits[2/f[x0], 10, 105][[1, 1 ;; 100]] (* Jean-François Alcover, Jul 16 2013 *)
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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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