A336199 - OEIS

%I #8 Jan 19 2022 21:28:46

%S 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,

%T 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,

%U 8,4,5,6,0,5,4,2,1,8,0,4,2,8,7,9,5,8,5

%N 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.

%C Solution to the three-dimensional version of Mrs. Miniver's problem.

%C The intersection volume is equal to 2/3 of the volume of each sphere, i.e., 8*Pi/9.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sphere-SphereIntersection.html">Sphere-Sphere Intersection</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mrs._Miniver%27s_problem">Mrs. Miniver's problem</a>.

%F Equals 4 * sin(arccos(-1/3)/3 - Pi/6).

%F The smaller of the two positive roots of the equation x^3 - 12*x + 16/3 = 0.

%e 0.452147427578415981828610831183181263247509153259677...

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jul 11 2020