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

1,3

Comments

See Ullisch link for a closed form. - Charles R Greathouse IV, Jul 08 2023

References

Ingo Ullisch, A Closed-Form Solution to the Geometric Goat Problem, The Mathematical Intelligencer volume 42 (2020), pp. 12-16.

Links

Table of n, a(n) for n=1..105.

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

Example

1.1587284730181215178...
Equals cos(A173201=1.9056957293.../2)*2. - Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010

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 *)

Prog

(PARI) cos(solve(x=1, 2, sin(x)-x*cos(x)-Pi/2)/2)*2 \\ Charles R Greathouse IV, Mar 03 2021

Crossrefs

Sequence in context: A199444 A005120 A362975 * A021067 A047914 A005480

Adjacent sequences: A133728 A133729 A133730 * A133732 A133733 A133734

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 21 2007

Status

approved