A383859 Central angle of the solution of the Tammes problem for 7 points on the sphere (in radians).

1, 3, 5, 9, 0, 7, 9, 8, 9, 7, 6, 3, 2, 6, 6, 0, 1, 4, 1, 8, 8, 5, 0, 0, 2, 8, 8, 1, 6, 4, 7, 3, 3, 2, 7, 5, 3, 7, 8, 3, 0, 2, 1, 4, 5, 9, 8, 6, 1, 2, 8, 2, 4, 9, 1, 3, 2, 6, 2, 8, 0, 7, 8, 3, 7, 1, 5, 9, 7, 3, 9, 8, 1, 6, 5, 8, 7, 6, 9, 7, 2, 4, 2, 6

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Laslo Hars, Numerical solutions of the Tammes problem for up to 60 points, Nov 2020, N=7.

K. Schutte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand eins Platz?, Math. Ann. 123 (1951) 96-124.

Wikipedia, Tammes problem

Index entries for transcendental numbers.

Formula

cos( this ) = cos(phi)/(1 - cos(phi)) where cos(phi) = A019819.

Equals Pi - arcsec(1 - csc(Pi/18)). - Paolo Xausa, Nov 24 2025

Example

1.3590798976326601418850028816473327537..

Maple

cos(4*Pi/9) ; %/(1-%) ; arccos(%) ; evalf(%, 120) ;

Mathematica

First[RealDigits[Pi - ArcSec[1 - Csc[Pi/18]], 10, 100]] (* Paolo Xausa, Nov 24 2025 *)

Prog

(PARI) acos(sin(Pi/18)/(1-sin(Pi/18))) \\ Charles R Greathouse IV, May 18 2026
(PARI) acos(polrootsreal(3*x^3 - 9*x^2 - 3*x + 1)[2]) \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A019819, A019669 (N=6), A381756 (N=8), A137914 (N=9), A340918 (N=10), A105199 (N=11 and N=12), A217695 (N=13), A383860 (N=14), A383861 (N=24).

Sequence in context: A067094 A272235 A058642 * A258086 A141251 A186190

Adjacent sequences: A383856 A383857 A383858 * A383860 A383861 A383862

Keyword

nonn,cons

Author

R. J. Mathar, May 12 2025

Status

approved