cp's OEIS Frontend

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.

%I A374837 #21 Jul 23 2024 14:57:57
%S A374837 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,
%T A374837 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,
%U A374837 3,1,5,9,5,5,4,4,8,8,2,3,5,8,6,0,3,5,3,3,6,8
%N 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.
%C A374837 See Theorem 1.1 in Bezdek and Daróczy-Kiss (2005).
%C A374837 See A374772 for an improved bound.
%H A374837 Paolo Xausa, <a href="/A374837/b374837.txt">Table of n, a(n) for n = 0..10000</a>
%H A374837 Károly Bezdek and Endre Daróczy-Kiss, <a href="https://doi.org/10.1007/s00605-004-0296-6">Finding the Best Face on a Voronoi Polyhedron--The Strong Dodecahedral Conjecture Revisited</a>, Monatshefte für Mathematik, Vol. 145, No. 3, July 2005, pp. 191-206.
%F A374837 Equals (30*arccos((sqrt(3)/2)*sin(Pi/5)) - 9*Pi)/(5*tan(Pi/5)).
%F A374837 Equals 4*Pi/A374838.
%e A374837 0.7783683851377739227957671666059435201971163186281...
%t A374837 First[RealDigits[(30*ArcCos[Sqrt[3]/2*Sin[Pi/5]] - 9*Pi)/(5*Tan[Pi/5]), 10, 100]]
%Y A374837 Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374772, A374838.
%K A374837 nonn,cons
%O A374837 0,1
%A A374837 _Paolo Xausa_, Jul 21 2024