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A255899
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Decimal expansion of Mrs. Miniver's constant.
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0
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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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Table of n, a(n) for n=0..104.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 62.
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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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Cf. A192408.
Sequence in context: A329986 A097897 A063761 * A019841 A064582 A197374
Adjacent sequences: A255896 A255897 A255898 * A255900 A255901 A255902
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KEYWORD
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nonn,cons,easy,changed
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AUTHOR
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Jean-François Alcover, Mar 10 2015
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STATUS
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approved
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