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

Author

Jean-François Alcover, Mar 10 2015

Keywords

• nonn
• cons
• easy

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).

Examples

			0.5298641692055537248682329895251421373003801320827289...
		

References

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

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, p. 62.

Crossrefs

Cf. A192408.

Programs

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

PARI

solve (x=0, 2, 2*acos(x/2) - (1/2)*x*sqrt(4 - x^2) - 2*Pi/3) \\ Michel Marcus, Mar 10 2015

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