A374838 Decimal expansion of Bezdek and Daróczy-Kiss's lower bound for the surface area of any Voronoi cell in an arbitrary packing of unit balls in the Euclidean 3-space.

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

Offset: 2

Author

Paolo Xausa, Jul 21 2024

Keywords

• nonn
• cons

Comments

See Theorem 1.1 in Bezdek and Daróczy-Kiss (2005).

See A374755 for an improved bound (the strong dodecahedral conjecture).

Examples

			16.144502852765379806937602328092933543868922009780...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Károly Bezdek and Endre Daróczy-Kiss, Finding the Best Face on a Voronoi Polyhedron--The Strong Dodecahedral Conjecture Revisited, Monatshefte für Mathematik, Vol. 145, No. 3, July 2005, pp. 191-206.

Crossrefs

Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374772, A374837.

Programs

Mathematica

First[RealDigits[20*Pi*Tan[Pi/5]/(30*ArcCos[Sqrt[3]/2*Sin[Pi/5]] - 9*Pi), 10, 100]]

Formula

Equals 20*Pi*tan(Pi/5)/(30*arccos(sqrt(3)/2*sin(Pi/5)) - 9*Pi).

Equals 4*Pi/A374837.