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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.
5
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
0,1
COMMENTS
See Theorem 1.1 in Bezdek and Daróczy-Kiss (2005).
See A374772 for an improved bound.
LINKS
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.
FORMULA
Equals (30*arccos((sqrt(3)/2)*sin(Pi/5)) - 9*Pi)/(5*tan(Pi/5)).
Equals 4*Pi/A374838.
EXAMPLE
0.7783683851377739227957671666059435201971163186281...
MATHEMATICA
First[RealDigits[(30*ArcCos[Sqrt[3]/2*Sin[Pi/5]] - 9*Pi)/(5*Tan[Pi/5]), 10, 100]]
CROSSREFS
Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374772, A374838.
Sequence in context: A011007 A226656 A019718 * A353973 A316139 A198992
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 21 2024
STATUS
approved