A374772 Decimal expansion of the upper bound of the density of sphere packing in the Euclidean 3-space resulting from the dodecahedral conjecture.

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

Offset: 0

Author

Paolo Xausa, Jul 19 2024

Keywords

• nonn
• cons

Comments

See A374753 for more information on the dodecahedral conjecture.

Also isoperimetric quotient (see A381671 for definition) of a regular dodecahedron. - Paolo Xausa, May 19 2025

Examples

			0.7546973993374058303916521059902293313424321921459...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Local Density.
• Index entries for transcendental numbers.

Crossrefs

Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374771, A374837, A374838.

Cf. A093825, A019699, A102769, A131595, A381671.

Programs

Mathematica

First[RealDigits[Pi*Sqrt[5 + Sqrt[5]]/(15*Sqrt[10]*(Sqrt[5] - 2)), 10, 100]]

PARI

Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)) \\ Charles R Greathouse IV, Feb 07 2025

Formula

Equals (4/3)*Pi/A374753 = 10*A019699/A374753.

Equals A374771/A102769.

Equals Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)).

Equals 4*Pi/A374755.

Equals 36*Pi*A102769^2/(A131595^3). - Paolo Xausa, May 19 2025