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

0,1

Links

Table of n, a(n) for n=0..90.

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

Example

0.971634742886224075941694947628...

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:

Crossrefs

Cf. A019669 (N=6), A383859 (N=7), A381756 (N=8), A137914 (N=9), A340918 (N=10), A105199 (N=11 and N=12). A217695 (N=13), A383861 (N=24).

Sequence in context: A329117 A389016 A309570 * A393891 A254249 A393374

Adjacent sequences: A383857 A383858 A383859 * A383861 A383862 A383863

Keyword

nonn,cons

Author

R. J. Mathar, May 12 2025

Status

approved