Recursive Definiton of PI

[Illuminator]

From "Numerical Recipes in C: The art of Scientific Computing"
This has to be one of the best math/computer science resources around. It covers everything from linear algebra and integration to Fourier and Wavelets and it provides c code for everything.

This is one sample from the book.
A recursive definition of PI:

 X(0) = 2^(1/2)
 Y(0) = 2^(1/4)
 PI(0) = 2+X(0)

 X(i+1) = 1/2 * [X(i)^(1/2) + X(i)^(-1/2)] 
 
 Y(i+1) = [Y(i) * X(i+1)^(1/2) + X(i+1)^(-1/2)]  /  [Y(i) + 1]

 PI(i+1) = PI(i) * [X(i+1) +1]  / [Y(i) +1]

as i -> infinity PI(i) -> PI
The sample in the book approxiamated PI to 2398 decimal places

[appi101]

Hi

How do we use this to find the value of Pi

Appi