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