Math help: Calculate pi using Gregory's Series on Beowulf?

[Chris Richard Adams]

Calulating Pi.	

I found a link to compute pi using Gregory's Series. It states the form
allowing quickest convergence
is..

	pi = 2*sqrt(3)*[ 1 - (1/(3*3)) + (1/(5*3^2)) - (1/(7*3^3)) ... ]

In the example for computing pi that comes with MPICH/MPI-Beowulf, I see
something like...

	Sum = Sum + 4 * [ 1 / ( 1 + ( 1/n * ( i - 0.5 ) )^2 ) ]

	where we iterate n times and i increments from 1 to n.	

	- then, pi = 1/n * sum

ANyone see how to get from Gregory's series to this form, or does this
form evolve from a different
approach?  I'll keep trying... any feedback is appreciated.

Chris