On the Python mailing list I got some great answers on how to generate the digits of PI. Here I sum them up.
Tichodroma forwarded me to http://mail.python.org/pipermail/edu-sig/2006-July/006810.html.
Here's a generator I coded up based on a paper by Gibbons: http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/spigot.pdf It's simple to code, but I think you have to read the paper to figure out what it's doing. (I just translated some code, so I really can't tell you :-) In the paper, this was done in a lazy functional language. I was mostly interested to see how it would translate to a Python generator. # pi.py -- imlementation of Gibbons' spigot algorithm for pi # John Zelle 4-5-06 def pi_digits(): """generator for digits of pi""" q,r,t,k,n,l = 1,0,1,1,3,3 while True: if 4*q+r-t < n*t: yield n q,r,t,k,n,l = (10*q,10*(r-n*t),t,k,(10*(3*q+r))/t-10*n,l) else: q,r,t,k,n,l = (q*k,(2*q+r)*l,t*l,k+1,(q*(7*k+2)+r*l)/(t*l),l+2) Here it is in action: >>> import pi >>> digits = pi.pidigits() >>> for i in range(30): print digits.next(), ... 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 >>> Since this uses long ints, it slows down considerably after a few thousand digits. You might want to use psyco when generating really "deep" digits. --John
It generates the digits of PI one after the other. It works well bit if you want lots of digits, it gets really slow.
E. Woiski suggested using the library SymPy.
sudo apt-get install python-sympy
>>> from sympy.mpmath import mp >>> mp.dps = 1000 # number of digits >>> +mp.pi # str(mp.pi)
Very fast and simple. The only problem might be that you need to install sympy.
Solution 3 (update, 20121128)
One of my students called G. Szegedi came up with this solution:
from bigfloat import precision import bigfloat str_pi = str(bigfloat.atan2(+0.0,-0.0,precision(1000)))
With the bigfloat package you can do high precision floating-point arithmetic.
I like simple solutions. So instead of generating the digits, I simply fetched the data from the web. This is a fast, efficient, and painless approach of the problem :) Visit http://newton.ex.ac.uk/research/qsystems/collabs/pi/, where you can download several data files.
For the lazy pigs
I made a script that downloads the data, parses them, and returns the digits as a string. Here it is.
Usage (get the first 30 digits of PI after the dot):
#!/usr/bin/env python from jabbapylib.math import pi def main(): digits = pi.get_digits_of(pi.PI3) # get 10^3 = 1000 digits print digits[:30] if __name__ == "__main__": main()
jabbapylib is here
Look at this verse:
How I want a drink alcoholic of course After the heavy lectures involving complex functions
Take the length of the words and you get the first 15 digits of PI. Here is the proof:
import sys import math s = """ How I want a drink alcoholic of course After the heavy lectures involving complex functions """ print [len(w) for w in s.split()] print math.pi
[3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9] 3.14159265359 # the last digit is rounded here
Read more on PI at http://www.eveandersson.com/pi/.
And if you didn’t know, here is the PI song :)
You can approximate the value of PI with 355/113. The first 6 decimal places are the same. It’s quite easy to memorize it: visualize 113355, split into two (113 and 355), then do the division.
>>> import math >>> math.pi 3.1415926535897931 >>> 355/113. 3.1415929203539825
Ref.: Kee Nethery at python-list.