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 A255899 Decimal expansion of Mrs. Miniver's constant. 1
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 487. LINKS Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 62. FORMULA 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]. EXAMPLE 0.5298641692055537248682329895251421373003801320827289... MATHEMATICA 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 PROG (PARI) solve (x=0, 2, 2*acos(x/2) - (1/2)*x*sqrt(4 - x^2) - 2*Pi/3) \\ Michel Marcus, Mar 10 2015 CROSSREFS Cf. A192408. Sequence in context: A329986 A097897 A063761 * A019841 A064582 A197374 Adjacent sequences:  A255896 A255897 A255898 * A255900 A255901 A255902 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Mar 10 2015 STATUS approved

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Last modified April 19 00:03 EDT 2021. Contains 343098 sequences. (Running on oeis4.)