This problem involves using the Monte Carlo method to find the
volume of a unit sphere embedded in d-dimensional Euclidean space.
My algorithm takes advantage of the symmetry, and finds the
volume in a part of the domain, and gets the final
answer by multiplying by
. This is accomplished by
randomly sprinkling points in the region
, and
looking at the frequency of occurance that the points fell in the
unit sphere. The volume for that portion of the unit sphere is
normalized against the volume of the domain, which is just 1.
The parallelism is obtained by allowing the processor to do this
task, and then sending the results to the controlling processor (0),
where the results (both volume and standard deviation of sampling) are
averaged.