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%I #7 Mar 17 2022 06:05:02
%S 1,5,2,0,5,4,8,9,5,2,8,8,3,9,8,8,2,6,1,7,2,4,7,6,3,7,7,9,3,5,5,3,6,9,
%T 4,5,9,1,2,6,1,0,8,8,3,8,8,9,0,5,2,0,3,4,7,8,9,6,5,7,0,0,7,8,7,2,8,9,
%U 8,5,6,5,3,4,9,3,2,1,4,8,9,6,7,4,2,9,1,0,2,6,9,7,7,9,6,5,5,6,5,4,0,7,9,2,8
%N Decimal expansion of the volume of intersection of 8 unit-radius spheres that have the vertices of a unit-side cube as centers.
%C The surface area of the solid formed by the intersection is A352455.
%C The solution to the two-dimensional version of this problem is A352453.
%H Kee-wai Lau, <a href="https://cms.math.ca/publications/crux/issue?volume=12&issue=9">Problem 1189</a>, Crux Mathematicorum, Vol. 12, No. 9 (1986), p. 242; <a href="https://cms.math.ca/publications/crux/issue?volume=14&issue=2">Solution to Problem 1189</a>, by Rex Westbrook, ibid., Vol. 14, No. 2 (1988), pp. 51-53.
%H Mathematics Stackexchange, <a href="https://math.stackexchange.com/questions/1164921/intersection-of-8-spheres-find-the-volume">Intersection of 8 spheres: find the volume</a>, 2015.
%H Missouri State University, <a href="http://people.missouristate.edu/lesreid/Adv08.html">Problem #8, Finding the Area (resp. Volume) of Overlapping Circles (resp. Spheres)</a>, Advanced Problem Archive; <a href="http://people.missouristate.edu/lesreid/AdvSol08.html">Solution to Problem #8</a>, by Ross Millikan.
%F Equals 97*Pi/12 - 27*arctan(sqrt(2)) + sqrt(2) - 1.
%F Equals 9*arctan(sqrt(2)/5) - 11*Pi/12 + sqrt(2) - 1.
%F 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.
%e 0.01520548952883988261724763779355369459126108838890...
%t RealDigits[97*Pi/12 - 27*ArcTan[Sqrt[2]] + Sqrt[2] - 1, 10, 100][[1]]
%Y Cf. A102888, A195696, A336198, A352453, A352455.
%K nonn,cons
%O -1,2
%A _Amiram Eldar_, Mar 16 2022
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