OFFSET
-1,2
COMMENTS
LINKS
Kee-wai Lau, Problem 1189, Crux Mathematicorum, Vol. 12, No. 9 (1986), p. 242; Solution to Problem 1189, by Rex Westbrook, ibid., Vol. 14, No. 2 (1988), pp. 51-53.
Mathematics Stackexchange, Intersection of 8 spheres: find the volume, 2015.
Missouri State University, Problem #8, Finding the Area (resp. Volume) of Overlapping Circles (resp. Spheres), Advanced Problem Archive; Solution to Problem #8, by Ross Millikan.
FORMULA
Equals 97*Pi/12 - 27*arctan(sqrt(2)) + sqrt(2) - 1.
Equals 9*arctan(sqrt(2)/5) - 11*Pi/12 + sqrt(2) - 1.
Equals 8 * Integral_{y=1/2..sqrt(2)/2} Integral_{x=1/2..sqrt(1-y^2-1/4)} (sqrt(1-x^2-y^2) - 1/2) dx dy.
EXAMPLE
0.01520548952883988261724763779355369459126108838890...
MATHEMATICA
RealDigits[97*Pi/12 - 27*ArcTan[Sqrt[2]] + Sqrt[2] - 1, 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 16 2022
STATUS
approved