A255899 Decimal expansion of Mrs. Miniver's constant.

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

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

Table of n, a(n) for n=0..104.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, 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].

Equals 2*cos(A336082 /2). - Robert FERREOL, Feb 18 2022

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 * A348408 A019841 A064582

Adjacent sequences: A255896 A255897 A255898 * A255900 A255901 A255902

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 10 2015

Status

approved