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A255899 Decimal expansion of Mrs. Miniver's constant. 1

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of Mrs. Miniver's constant.

%C 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).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 487.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 62.

%F 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].

%e 0.5298641692055537248682329895251421373003801320827289...

%t 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

%o (PARI) solve (x=0, 2, 2*acos(x/2) - (1/2)*x*sqrt(4 - x^2) - 2*Pi/3) \\ _Michel Marcus_, Mar 10 2015

%Y Cf. A192408.

%K nonn,cons,easy

%O 0,1

%A _Jean-Fran├žois Alcover_, Mar 10 2015

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Last modified May 12 16:02 EDT 2021. Contains 343825 sequences. (Running on oeis4.)