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A255899
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Decimal expansion of Mrs. Miniver's constant.
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2
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5, 2, 9, 8, 6, 4, 1, 6, 9, 2, 0, 5, 5, 5, 3, 7, 2, 4, 8, 6, 8, 2, 3, 2, 9, 8, 9, 5, 2, 5, 1, 4, 2, 1, 3, 7, 3, 0, 0, 3, 8, 0, 1, 3, 2, 0, 8, 2, 7, 2, 8, 9, 0, 5, 7, 5, 7, 4, 8, 9, 7, 8, 6, 5, 8, 4, 1, 8, 0, 5, 0, 1, 7, 4, 1, 3, 7, 7, 2, 7, 7, 9, 4, 5, 4, 6, 9, 9, 7, 0, 4, 6, 7, 4, 9, 2, 3, 6, 8, 8, 8, 2, 1, 1, 8
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OFFSET
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0,1
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COMMENTS
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This constant is the solution to an elementary problem involving two overlapping circles, known as "Mrs. Miniver's problem" (cf. S. R. Finch, p. 487), the value of the solution being the distance between the centers of the two circles (see the picture by L. A. Graham in A192408).
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 487.
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LINKS
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FORMULA
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The unique root of the equation 2*arccos(x/2) - (1/2)*x*sqrt(4 - x^2) = 2*Pi/3 in the interval [0,2].
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EXAMPLE
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0.5298641692055537248682329895251421373003801320827289...
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MATHEMATICA
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d = x /. FindRoot[2*ArcCos[x/2] - (1/2)*x*Sqrt[4 - x^2] == 2*Pi/3, {x, 1/2}, WorkingPrecision -> 105]; RealDigits[d] // First
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PROG
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(PARI) solve (x=0, 2, 2*acos(x/2) - (1/2)*x*sqrt(4 - x^2) - 2*Pi/3) \\ Michel Marcus, Mar 10 2015
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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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