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

Author

Amiram Eldar, Jul 11 2020

Keywords

• nonn
• cons

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.

Examples

			0.452147427578415981828610831183181263247509153259677...
		

Links

• Eric Weisstein's World of Mathematics, Sphere-Sphere Intersection.
• Wikipedia, Mrs. Miniver's problem.

Crossrefs

Cf. A019673, A019699, A133749, A156546, A255899.

Programs

Mathematica

RealDigits[4 * Sin[ArcCos[-1/3]/3 - Pi/6], 10, 100][[1]]

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.