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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.

%I A374838 #22 Jul 23 2024 20:32:57
%S A374838 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,
%T A374838 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,
%U A374838 1,3,7,1,5,9,4,4,8,8,5,0,5,6,8,4,1,9,0,5,9,2
%N 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.
%C A374838 See Theorem 1.1 in Bezdek and Daróczy-Kiss (2005).
%C A374838 See A374755 for an improved bound (the strong dodecahedral conjecture).
%H A374838 Paolo Xausa, <a href="/A374838/b374838.txt">Table of n, a(n) for n = 2..10000</a>
%H A374838 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 A374838 Equals 20*Pi*tan(Pi/5)/(30*arccos(sqrt(3)/2*sin(Pi/5)) - 9*Pi).
%F A374838 Equals 4*Pi/A374837.
%e A374838 16.144502852765379806937602328092933543868922009780...
%t A374838 First[RealDigits[20*Pi*Tan[Pi/5]/(30*ArcCos[Sqrt[3]/2*Sin[Pi/5]] - 9*Pi), 10, 100]]
%Y A374838 Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374772, A374837.
%K A374838 nonn,cons
%O A374838 2,2
%A A374838 _Paolo Xausa_, Jul 21 2024