A374837 Decimal expansion of Bezdek and Daróczy-Kiss's upper bound for the surface area density of a unit ball in any face cone of a Voronoi cell in an arbitrary packing of unit balls in the Euclidean 3-space.

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

Offset: 0

Author

Paolo Xausa, Jul 21 2024

Keywords

• nonn
• cons

Comments

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

See A374772 for an improved bound.

Examples

			0.7783683851377739227957671666059435201971163186281...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..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, A374838.

Programs

Mathematica

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

Formula

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

Equals 4*Pi/A374838.