A383860 Central angle of the solution of the Tammes problem for 14 points on the sphere (in radians).
9, 7, 1, 6, 3, 4, 7, 4, 2, 8, 8, 6, 2, 2, 4, 0, 7, 5, 9, 4, 1, 6, 9, 4, 9, 4, 7, 6, 2, 8, 5, 4, 1, 1, 3, 8, 1, 7, 9, 0, 1, 0, 6, 8, 2, 7, 6, 8, 4, 7, 8, 2, 0, 7, 0, 2, 6, 8, 0, 3, 3, 4, 8, 1, 3, 5, 4, 5, 5, 6, 5, 0, 7, 3, 5, 4, 4, 0, 3, 2, 9, 4, 6, 3, 9, 9, 5, 3, 9, 9, 4
Offset: 0
Examples
0.971634742886224075941694947628...
Links
- Laslo Hars, Numerical solutions of the Tammes problem for up to 60 points, Nov 2020, N=14.
- O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015) 460-468.
- Wikipedia, Tammes problem
Crossrefs
Programs
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Maple
Digits := 120 ; g := proc(c,x) 2*arccot(c*tan(x/2)) ; end proc: f := proc(x) local c,x1,x2,x3,x4,x5 ; c := cos(x)/(1-cos(x)) ; x1 := Pi-x ; x2 := g(c,x1) ; x3 := 2*Pi-2*x-x2 ; x4 := g(c,x3) ; x5 := 2*Pi-x-2*x4 ; 2*Pi-2*x-x3-g(c,x5) ; end proc: x := 1.2 ; y := 1.21 ; for i from 1 to 500 do z := (x+y)/2 ; if f(z) > 0. then x := z ; else y := z ; end if; cos(z)/(1-cos(z)) ; if modp(i,20) =0 then arccos(%) ; evalf(%,120) ; print(%) ; end if; if x > y then break ; end if; end do: