OFFSET
1,3
COMMENTS
In his habilitation thesis from 1963, Ludwig Danzer provided an interval from 1.1544786 to 1.1544795 (rounded) for this value.
REFERENCES
Ludwig Danzer, Endliche Punktmengen auf der 2-Sphaere mit moeglichst grossem Minimalabstand. Habilitationsschrift, Universitaet Goettingen, 1963. See link for the English translation.
LINKS
Ludwig Danzer, Finite point-sets on S^2 with minimum distance as large as possible, Discrete Mathematics, Volume 60, June-July 1986, Pages 3-66, Table 1, page 63.
Hugo Pfoertner, Visualization of the optimal configuration, (2001).
Teruhisa Sugimoto and Masaharu Tanemura, Exact value of Tammes problem for N=10, arXiv:1509.01768 [math.MG], 12 Sep 2015.
FORMULA
atan(sqrt((4/sqrt(3))*cos((1/3)*atan(sqrt(3*229)/9)) + 3))
EXAMPLE
1.1544798334192707378319618404230211144893004873633425122414214417...
PROG
(PARI) atan(sqrt((4/sqrt(3))*cos((1/3)*atan(sqrt(3*229)/9))+3))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Jan 30 2021
STATUS
approved