Recursive Definiton of PI
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:
Code:
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
