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%I #5 Jun 23 2022 13:49:23
%S 8,6,8,4,1,0,0,4,8,8,2,4,6,1,3,5,4,3,9,7,2,8,3,7,1,1,6,2,5,7,6,9,3,0,
%T 8,2,3,8,6,3,6,4,3,9,3,0,7,0,9,8,2,4,8,6,8,0,9,5,3,2,9,6,1,9,3,5,2,9,
%U 4,5,7,5,4,9,1,5,2,2,0,7,9,4,0,7,1,9,2,4,6,2,3,3,6,2,4,6,1,9,3,6,0,4,5,7,6
%N Decimal expansion of the volume of the region that represents the set of points in a unit cube that are closer to the center of the cube than to the closest face.
%C The shape is formed by the intersection of 6 paraboloids.
%H Nicholas R. Baeth, Loren Luther, and Rhonda McKee, <a href="http://www.jstor.org/stable/10.4169/math.mag.90.4.243">The Downtown Problem: Variations on a Putnam Problem</a>, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.
%H Amiram Eldar, <a href="/A355185/a355185.jpg">Illustration</a>.
%F Equals (Pi + 4 - 5*sqrt(3) + (1+sqrt(3))*sqrt((2+sqrt(3))/8))/4.
%e 0.08684100488246135439728371162576930823863643930709...
%t RealDigits[(Pi + 4 - 5*Sqrt[3] + (1+Sqrt[3])*Sqrt[(2+Sqrt[3])/8])/4, 10, 100][[1]]
%Y Cf. A093066, A097047, A355183 (2D analog).
%K nonn,cons
%O -1,1
%A _Amiram Eldar_, Jun 23 2022