

A336199


Decimal expansion of the distance between the centers of two unitradius 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
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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

Table of n, a(n) for n=0..86.
Eric Weisstein's World of Mathematics, SphereSphere Intersection.
Wikipedia, Mrs. Miniver's problem.


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

Cf. A019673, A019699, A133749, A156546, A255899.
Sequence in context: A156890 A320480 A163531 * A267095 A016715 A337192
Adjacent sequences: A336196 A336197 A336198 * A336200 A336201 A336202


KEYWORD

nonn,cons


AUTHOR

Amiram Eldar, Jul 11 2020


STATUS

approved



