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

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

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Jul 11 2020

STATUS

approved