A133731 Decimal expansion of goat tether length to graze half a unit field.
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, 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, 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
Offset: 1
Examples
1.1587284730181215178...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.2, p. 487.
- Ingo Ullisch, A Closed-Form Solution to the Geometric Goat Problem, The Mathematical Intelligencer volume 42 (2020), pp. 12-16.
Links
- Michael Johannes Latsky, Table of n, a(n) for n = 1..20000
- M. Fraser, A tale of two goats, Math. Mag., 55 (1982), 221-227. Has extensive bibliography.
- James Grime and Brady Haran, The Goat Problem, Numberphile video (2023).
- Graham Jameson and Nicholas Jameson, Goats and birds, The Mathematical Gazette, Volume 101, Issue 551 (July 2017), pp. 296-300.
- Gerd Lamprecht, A133731=cos(A173201/2)*2; 10000 digits [Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010]
- Gerd Lamprecht, Iterationsrechner mit Algorithmus [Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010]
- Eric Weisstein's World of Mathematics, Goat Problem.
Programs
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Mathematica
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 *)
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PARI
cos(solve(x=1,2,sin(x)-x*cos(x)-Pi/2)/2)*2 \\ Charles R Greathouse IV, Mar 03 2021
Formula
Equals cos(A173201/2)*2. - Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010
Comments