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%I #27 Jul 08 2023 20:56:39
%S 1,1,5,8,7,2,8,4,7,3,0,1,8,1,2,1,5,1,7,8,2,8,2,3,3,5,0,9,9,3,3,5,0,9,
%T 1,4,9,6,8,8,2,9,2,2,6,6,4,9,2,0,9,6,5,1,1,8,2,0,6,9,5,8,8,4,8,2,0,6,
%U 6,9,8,0,2,5,5,9,1,9,6,0,9,3,1,9,9,3,2,1,6,1,0,7,3,0,8,6,0,4,3,8,1,7,5,9,6
%N Decimal expansion of goat tether length to graze half a unit field.
%C See Ullisch link for a closed form. - _Charles R Greathouse IV_, Jul 08 2023
%D Ingo Ullisch, A Closed-Form Solution to the Geometric Goat Problem, The Mathematical Intelligencer volume 42 (2020), pp. 12-16.
%H M. Fraser, <a href="http://www.jstor.org/stable/2690163">A tale of two goats</a>, Math. Mag., 55 (1982), 221-227. Has extensive bibliography.
%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=ZdQFN2XKeKI">The Goat Problem</a>, Numberphile video (2023)
%H Graham Jameson and Nicholas Jameson, <a href="http://nojameson.net/goat.pdf">Goats and birds</a>, The Mathematical Gazette, Volume 101, Issue 551 (July 2017), pp. 296-300.
%H Gerd Lamprecht, <a href="http://www.gerdlamprecht.de/langeZahlen/1158728473.pdf">A133731=cos(A173201/2)*2; 10000 digits</a> [Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010]
%H Gerd Lamprecht, <a href="http://www.gerdlamprecht.de/Roemisch_JAVA.htm#ZZZZZ0004">Iterationsrechner mit Algorithmus</a> [Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoatProblem.html">Goat Problem</a>
%e 1.1587284730181215178...
%e Equals cos(A173201=1.9056957293.../2)*2. - Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010
%t A173201 = x /. FindRoot[(-x*Cos[x] + Sin[x] - Pi/2)/(Sin[x]*x), {x, 1}, WorkingPrecision -> 105]; RealDigits[2*Cos[A173201/2] ][[1]] (* _Jean-François Alcover_, Oct 31 2012 *)
%o (PARI) cos(solve(x=1,2,sin(x)-x*cos(x)-Pi/2)/2)*2 \\ _Charles R Greathouse IV_, Mar 03 2021
%K nonn,cons
%O 1,3
%A _Eric W. Weisstein_, Sep 21 2007
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