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A336199
Decimal expansion of the distance between the centers of two unit-radius spheres such that the volume of intersection is equal to the sum of volumes of the two nonoverlapping parts.
0
4, 5, 2, 1, 4, 7, 4, 2, 7, 5, 7, 8, 4, 1, 5, 9, 8, 1, 8, 2, 8, 6, 1, 0, 8, 3, 1, 1, 8, 3, 1, 8, 1, 2, 6, 3, 2, 4, 7, 5, 0, 9, 1, 5, 3, 2, 5, 9, 6, 7, 7, 5, 6, 6, 8, 0, 7, 7, 6, 7, 0, 4, 5, 7, 6, 0, 0, 6, 8, 4, 5, 6, 0, 5, 4, 2, 1, 8, 0, 4, 2, 8, 7, 9, 5, 8, 5
OFFSET
0,1
COMMENTS
Solution to the three-dimensional version of Mrs. Miniver's problem.
The intersection volume is equal to 2/3 of the volume of each sphere, i.e., 8*Pi/9.
LINKS
Eric Weisstein's World of Mathematics, Sphere-Sphere Intersection.
FORMULA
Equals 4 * sin(arccos(-1/3)/3 - Pi/6).
The smaller of the two positive roots of the equation x^3 - 12*x + 16/3 = 0.
EXAMPLE
0.452147427578415981828610831183181263247509153259677...
MATHEMATICA
RealDigits[4 * Sin[ArcCos[-1/3]/3 - Pi/6], 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 11 2020
STATUS
approved