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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 (list; constant; graph; refs; listen; history; text; internal format)
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, Sphere-Sphere 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

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Last modified June 20 15:48 EDT 2021. Contains 345165 sequences. (Running on oeis4.)