

A217695


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


1



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

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


LINKS

Table of n, a(n) for n=0..100.
Oleg Musin and Alexey Tarasov, The strong thirteen spheres problem, Discrete & Computational Geometry 48:1 (2012), pp. 128141. doi:10.1007/s0045401193922


EXAMPLE

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


MATHEMATICA

digits = 101; x0 = x /. FindRoot[2*Tan[3*Pi/8x/4](12*Cos[x])/Cos[x]^2 == 0, {x, 6/5}, WorkingPrecision > digits+1]; ArcCos[Cos[x0]/(1Cos[x0])] // RealDigits[#, 10, digits]& // First (* JeanFrançois Alcover, Feb 20 2014, after PARI *)


PROG

(PARI) (a>acos(cos(a)/(1cos(a))))(solve(x=1, 2, 2*tan(3*Pi/8x/4)(12*cos(x))/cos(x)^2))


CROSSREFS

Sequence in context: A085984 A157245 A072908 * A197390 A298520 A270712
Adjacent sequences: A217692 A217693 A217694 * A217696 A217697 A217698


KEYWORD

nonn,cons


AUTHOR

Charles R Greathouse IV, Mar 20 2013


STATUS

approved



