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

Author

Hugo Pfoertner, Jan 30 2021

Keywords

• nonn
• cons

Comments

In his habilitation thesis from 1963, Ludwig Danzer provided an interval from 1.1544786 to 1.1544795 (rounded) for this value.

Examples

			1.1544798334192707378319618404230211144893004873633425122414214417...
		

References

• Ludwig Danzer, Endliche Punktmengen auf der 2-Sphaere mit moeglichst grossem Minimalabstand. Habilitationsschrift, Universitaet Goettingen, 1963. See link for the English translation.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A080865, A217695, A339262.

Programs

Mathematica

First[RealDigits[ArcTan[Sqrt[4/Sqrt[3]*Cos[ArcTan[Sqrt[3*229]/9]/3] + 3]], 10, 100]] (* Paolo Xausa, Feb 27 2025 *)

PARI

atan(sqrt((4/sqrt(3))*cos((1/3)*atan(sqrt(3*229)/9))+3))

Formula

atan(sqrt((4/sqrt(3))*cos((1/3)*atan(sqrt(3*229)/9)) + 3))