A383860 -id:A383860 - cp's OEIS frontend

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

R. J. Mathar, May 12 2025

			1.3590798976326601418850028816473327537..

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

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).

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

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

A383861 Central angle of the solution of the Tammes problem for 24 points on the sphere (in radians).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, May 12 2025

			0.762547738750982556743106092114...

Laslo Hars, Numerical solutions of the Tammes problem for up to 60 points, Nov 2020, N=24.
R. M. Robinson, Arrangements of 24 points on the sphere, Math. Ann. 144 (1961) 17-48.
Wikipedia, Tammes problem

Cf. A058265, A019669 (N=6), A383859 (N=7), A381756 (N=8), A137914 (N=9), A340918 (N=10), A105199 (N=11 and N=12). A217695 (N=13), A383860 (N=14).

t := (1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3))/3 ; arccos((t-1)/(3-t)) ; evalf(%,120);

cos( this ) = (t-1)/(3-t) where t=A058265.

cp's OEIS Frontend

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

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