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.

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

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