A379394 Decimal expansion of the area of the convex hull of a circle of circumference 1 and a line segment of length 1/2 with midpoint at the circle center.

9, 6, 3, 2, 9, 6, 1, 6, 5, 2, 1, 8, 7, 8, 2, 4, 7, 0, 1, 8, 4, 3, 6, 4, 8, 9, 1, 7, 5, 3, 8, 1, 3, 4, 4, 9, 7, 0, 3, 1, 6, 2, 6, 6, 9, 7, 9, 7, 4, 8, 2, 1, 7, 9, 6, 4, 5, 8, 9, 6, 7, 8, 4, 2, 8, 8, 0, 8, 7, 9, 0, 9, 0, 6, 7, 0, 4, 3, 1, 3, 9, 7, 1, 5, 6, 5, 8, 0, 3, 0, 9, 8, 8, 8, 7, 3, 3, 3, 2, 5

Offset

-1,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4.2, p. 495.

Links

Table of n, a(n) for n=-1..98.

Formula

Equals sqrt(Pi^2-4) + Pi - 2*arccos(2/Pi))/(4*Pi^2).

Example

0.096329616521878247018436489175381344970316266979748...

Mathematica

RealDigits[(Sqrt[Pi^2-4]+Pi-2ArcCos[2/Pi])/(4Pi^2), 10, 100][[1]]

Crossrefs

Cf. A000796, A002388, A060294, A212002, A275477.

Sequence in context: A068925 A175616 A200232 * A198997 A271172 A019683

Adjacent sequences: A379391 A379392 A379393 * A379395 A379396 A379397

Keyword

nonn,cons

Author

Stefano Spezia, Dec 22 2024

Status

approved