A086118 Decimal expansion of Pi/2 + 2/Pi.

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

Offset

1,1

Comments

Lower limit in the moving sofa problem.

This is the expected angle of a random rotation [Salamin]. - Bill Gosper, Oct 20 2013

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 8.12, pp. 519-523.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Steven R. Finch, Moving Sofa Constant, Mathcad Library. [Wayback Machine link]

Math Stackexchange, Mean value of the rotation angle is 126.5 degrees, 2013.

Eugene Salamin, Application of quaternions to computation with rotations, Working Paper, Stanford AI Lab, 1979.

Marc B. Reynolds, Volume element of SO(3) and average uniform random rotation angle, 2017.

Hansklaus Rummler, On the distribution of rotation angles how great is the mean rotation angle of a random rotation?, The Mathematical Intelligencer, Vol. 24, No. 4 (2002), pp. 6-11; alternative link.

Eric Weisstein's World of Mathematics, Hammersley Sofa.

Eric Weisstein's World of Mathematics, Moving Sofa Problem.

Wikipedia, Moving sofa problem.

Index entries for transcendental numbers.

Example

2.2074160991624779623068567451298088902364232826493787...

Mathematica

RealDigits[Pi/2 + 2/Pi, 10, 100][[1]] (* Amiram Eldar, Mar 17 2023 *)

Prog

(PARI) 2/Pi+Pi/2 \\ Charles R Greathouse IV, Oct 01 2022

Crossrefs

Cf. A128463 (a better lower bound), A336083, A361605.

Sequence in context: A135006 A323675 A243492 * A104986 A060007 A021457

Adjacent sequences: A086115 A086116 A086117 * A086119 A086120 A086121

Keyword

nonn,cons,easy,changed

Author

Eric W. Weisstein, Jul 10 2003

Status

approved