A255899 - OEIS

%I #22 Feb 19 2022 03:41:47

%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>, arXiv:2001.00578 [math.HO], 2020-2021, 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].

%F Equals 2*cos(A336082 /2). - _Robert FERREOL_, Feb 18 2022

%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-François Alcover_, Mar 10 2015