A217695 Decimal expansion of largest angular separation (in radians) between 13 points on a unit sphere.

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

Offset: 0

Author

Charles R Greathouse IV, Mar 20 2013

Keywords

• nonn
• cons

Comments

Since this is less than Pi/3, the kissing number in three dimensions is 12 rather than 13. Related to the Tammes problem.

Examples

			0.99722359243811916365477045057612201455032449373301442534628103416840073521118... radians = 57.1367030... degrees.
		

Links

• Oleg Musin and Alexey Tarasov, The strong thirteen spheres problem, Discrete & Computational Geometry 48:1 (2012), pp. 128-141. doi:10.1007/s00454-011-9392-2

Crossrefs

Cf. A257479.

Programs

Mathematica

digits = 101; x0 = x /. FindRoot[2*Tan[3*Pi/8-x/4]-(1-2*Cos[x])/Cos[x]^2 == 0, {x, 6/5}, WorkingPrecision -> digits+1]; ArcCos[Cos[x0]/(1-Cos[x0])] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 20 2014, after PARI *)

PARI

(a->acos(cos(a)/(1-cos(a))))(solve(x=1,2,2*tan(3*Pi/8-x/4)-(1-2*cos(x))/cos(x)^2))