A396022 Decimal expansion of (2+sqrt(2))/(2*Pi).

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

Offset

0,1

Comments

The probability that Buffon's needle (see A060294), bent at its midpoint at a 90 degrees angle, will land on a line when dropped onto a floor with parallel lines spaced at a distance equal to the length of the needle.

Links

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

Uwe Bäsel, Buffon's problem with a pivot needle, Elemente der Mathematik, Vol. 70, No. 2 (2015), pp. 67-70. See Remark 1, p. 70.

Robert Nelson, Pictures, Probability, and Paradox, The Two-Year College Mathematics Journal, Vol. 10, No. 3 (1979), pp. 182-190. See Problem 6, pp. 187-188.

Eric Weisstein's World of Mathematics, Buffon's needle problem.

Wikipedia, Buffon's needle problem.

Index entries for transcendental numbers.

Example

0.543388965223067188926567324496713869735062828969718...

Mathematica

RealDigits[(2+Sqrt[2])/(2*Pi), 10, 120][[1]]

Prog

(PARI) (2+sqrt(2))/(2*Pi)

Crossrefs

Cf. A060294, A089491, A396023.

Sequence in context: A321028 A351169 A395136 * A263356 A061836 A021188

Adjacent sequences: A396019 A396020 A396021 * A396023 A396024 A396025

Keyword

nonn,cons

Author

Amiram Eldar, May 14 2026

Status

approved