From: Jaap Spies <j.spies@hccnet.nl>
Subject: Re: How to calculate Pi?
Date: Sun, 15 Oct 2000 01:54:53 +0200
Newsgroups: sci.math.symbolic
Summary: [missing]

lcamargo@nutecnet.com.br wrote:
> 
> I would like to know how to calculate, how to compute
> the pi number with n decimal digits, say 1000 places.
> 
> I intent to follow Machin formula.
> 
>    pi = 16 arctan (1/5) - 4 arctan (1/239)
>    where arctan (x) = x - x^3/3 + x^5/5 - x^7/7 + ...
> 
> The common known algorithm is:
> 
>    a = 16 / 5
>    b = 4 / 239
>    pi = a - b
>    sign = -1
>    FOR n = 3 TO ... STEP 2
>        a = a / 25
>        b = b / 57121
>        pi = pi + sign * (a - b) / n
>        sign = -sign
>    NEXT n
> 
> We know the computer does not support this amount of
> numbers, and this is exactly the question: how to make
> the concatenation of the decimal digits. I would like
> to know an easy method, step-by-step, for beginner
> user (not for advanced user). Preferentially with a
> simple text.
> 
> Can anyone here help me?
> 
> Thanks.
> Luiz
> 
> Sent via Deja.com http://www.deja.com/
> Before you buy.

Try this small Python Program

# After Petrarca, Shakespeare, Milton, Drs. P and many, many others,
# a sonnet has 14 lines and a certain rhyme scheme.

# Jacques Bens presented in 1965 in Paris the pi-sonnet with
# 3,1,4,1 and 5 lines, but the ultimate pi-poem I found in
# Brown's Python Annotated Archives p. 12:

# Based on a algorithm of Lambert Meertens (remember those days of the
# B -> ABC-programming language!!!)

import sys

def main():
    k, a, b, a1, b1 = 2L, 4L, 1L, 12L, 4L
    while 1:
        p, q, k = k*k, 2L*k+1L, k+1L
        a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1
        d, d1 = a/b, a1/b1
        while d == d1:
            output(d)
            a, a1 = 10L*(a%b), 10L*(a1%b1)
            d, d1 = a/b, a1/b1

def output(d):
    sys.stdout.write(`int(d)`)
    sys.stdout.flush()

main()

# Reading/writing Python source often gives me the impression of
# reading/writing a poem!
# Layout, indentation, rythm, I like the look and feel!

# What does this tiny program do? It is not a sonnet, even not a
# pi-sonnet, but it surely produces Pi!

# The poem ( sorry, the program) needs some explanation.
# As a mathematician I recognize the continued fraction, odd/even,
# squares and all that matters.
# But it is a miracle! A few lines of Python code producing
# a infinity of pi-digits!


# Jaap Spies

# Keep Peace in Mind

# What is Python?
# See http://www.python.org