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A355185
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.
2
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, 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, 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
OFFSET
-1,1
COMMENTS
The shape is formed by the intersection of 6 paraboloids.
LINKS
Nicholas R. Baeth, Loren Luther, and Rhonda McKee, The Downtown Problem: Variations on a Putnam Problem, Mathematics Magazine, Vol. 90, No. 4 (2017), pp. 243-257.
Amiram Eldar, Illustration.
FORMULA
Equals (Pi + 4 - 5*sqrt(3) + (1+sqrt(3))*sqrt((2+sqrt(3))/8))/4.
EXAMPLE
0.08684100488246135439728371162576930823863643930709...
MATHEMATICA
RealDigits[(Pi + 4 - 5*Sqrt[3] + (1+Sqrt[3])*Sqrt[(2+Sqrt[3])/8])/4, 10, 100][[1]]
CROSSREFS
Cf. A093066, A097047, A355183 (2D analog).
Sequence in context: A159627 A302682 A011298 * A188655 A282152 A191909
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 23 2022
STATUS
approved