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%I #29 Aug 12 2023 12:39:50
%S 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,
%T 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,
%U 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
%N Decimal expansion of Pi/2 + 2/Pi.
%C Lower limit in the moving sofa problem.
%C This is the expected angle of a random rotation [Salamin]. - _Bill Gosper_, Oct 20 2013
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 8.12, pp. 519-523.
%H Alois P. Heinz, <a href="/A086118/b086118.txt">Table of n, a(n) for n = 1..10000</a>
%H Steven R. Finch, <a href="https://web.archive.org/web/20080107101427/http://mathcad.com/library/constants/sofa.htm">Moving Sofa Constant</a>, Mathcad Library. [Wayback Machine link]
%H Math Stackexchange, <a href="https://math.stackexchange.com/questions/464419/mean-value-of-the-rotation-angle-is-126-5%C2%B0">Mean value of the rotation angle is 126.5 degrees</a>, 2013.
%H Eugene Salamin, <a href="https://theworld.com/~sweetser/quaternions/ps/stanfordaiwp79-salamin.pdf">Application of quaternions to computation with rotations</a>, Working Paper, Stanford AI Lab, 1979.
%H Marc B. Reynolds, <a href="https://marc-b-reynolds.github.io/quaternions/2017/11/10/AveRandomRot.html">Volume element of SO(3) and average uniform random rotation angle</a>, 2017.
%H Hansklaus Rummler, <a href="https://doi.org/10.1007/BF03025318">On the distribution of rotation angles how great is the mean rotation angle of a random rotation?</a>, The Mathematical Intelligencer, Vol. 24, No. 4 (2002), pp. 6-11; <a href="https://core.ac.uk/download/pdf/159153606.pdf">alternative link</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MovingSofaProblem.html">Moving Sofa Problem</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Moving_sofa_problem">Moving sofa problem</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e 2.2074160991624779623068567451298088902364232826493787...
%t RealDigits[Pi/2 + 2/Pi, 10, 100][[1]] (* _Amiram Eldar_, Mar 17 2023 *)
%o (PARI) 2/Pi+Pi/2 \\ _Charles R Greathouse IV_, Oct 01 2022
%Y Cf. A128463 (a better lower bound), A336083, A361605.
%K nonn,cons,easy
%O 1,1
%A _Eric W. Weisstein_, Jul 10 2003
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