A340918 Decimal expansion of largest angular separation (in radians) between 10 points on a unit sphere.

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

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

Table of n, a(n) for n=1..87.

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

Cf. A080865, A217695, A339262.

Sequence in context: A019842 A357418 A303270 * A244046 A255332 A071419

Adjacent sequences: A340915 A340916 A340917 * A340919 A340920 A340921

Keyword

nonn,cons

Author

Hugo Pfoertner, Jan 30 2021

Status

approved