Simple π calculation [2010-01] (from Pythagorean theorem)

pi.py

#!/usr/bin/env python
# encoding: utf-8
from __future__ import division, with_statement
import sys

from math import sqrt, pi

def calculatePi(samples):
	samples = int(samples)
	
	if samples < 2:
		raise ValueError("Minimum of two samples required.")
	
	radius = 1
	
	points = []
	
	for n in range(samples):
		x = (2 * n * radius / (samples - 1)) - radius
		points.append((x, sqrt(radius ** 2 - x ** 2)))
	
	perimiter = 0
	
	for n in range(len(points) - 1):
		perimiter += sqrt((points[n + 1][0] - points[n][0]) ** 2 + (points[n + 1][1] - points[n][1]) ** 2)
	
	return perimiter / radius

def main():	
	print " Samples Calculated Variation"
	print " ------- ---------- ---------"
	
	sampleRange  = list(range(    2,     10,     1))
	sampleRange += list(range(   10,    100,    10))
	sampleRange += list(range(  100,   1000,   100))
	sampleRange += list(range( 1000,  10000,  1000))
	sampleRange += list(range(10000, 100001, 10000))
	
	for samples in sampleRange:
		ourPi = calculatePi(samples)
		print " %6i  %9.7f %9.7f" % (samples, ourPi, ourPi - pi)

if __name__ == "__main__": sys.exit(main())

pi.txt

 Samples Calculated Variation
 ------- ---------- ---------
      2  2.0000000 -1.1415927
      3  2.8284271 -0.3131655
      4  2.9760677 -0.1655249
      5  3.0352762 -0.1063165
      6  3.0659554 -0.0756372
      7  3.0842529 -0.0573398
      8  3.0961950 -0.0453977
      9  3.1044961 -0.0370966
     10  3.1105417 -0.0310509
     20  3.1315167 -0.0100760
     30  3.1362561 -0.0053366
     40  3.1381728 -0.0034198
     50  3.1391652 -0.0024275
     60  3.1397558 -0.0018368
     70  3.1401405 -0.0014521
     80  3.1404075 -0.0011852
     90  3.1406016 -0.0009911
    100  3.1407479 -0.0008447
    200  3.1412963 -0.0002963
    300  3.1414318 -0.0001609
    400  3.1414883 -0.0001044
    500  3.1415180 -0.0000746
    600  3.1415359 -0.0000567
    700  3.1415477 -0.0000450
    800  3.1415558 -0.0000368
    900  3.1415618 -0.0000309
   1000  3.1415663 -0.0000263
   2000  3.1415833 -0.0000093
   3000  3.1415876 -0.0000051
   4000  3.1415894 -0.0000033
   5000  3.1415903 -0.0000024
   6000  3.1415909 -0.0000018
   7000  3.1415912 -0.0000014
   8000  3.1415915 -0.0000012
   9000  3.1415917 -0.0000010
  10000  3.1415918 -0.0000008
  20000  3.1415924 -0.0000003
  30000  3.1415925 -0.0000002
  40000  3.1415925 -0.0000001
  50000  3.1415926 -0.0000001
  60000  3.1415926 -0.0000001
  70000  3.1415926 -0.0000000
  80000  3.1415926 -0.0000000
  90000  3.1415926 -0.0000000
 100000  3.1415926 -0.0000000