Relevant code and results for yesterday's post on 'Estimating the value of \pi'

In [58]:

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

In [77]:

a = 100
alist = np.arange(0,a+1,1)
anotherlist = np.zeros(iterations)
count = 0.
iterations = 100
for i in xrange(iterations):
    tempx = np.random.choice(alist)
    tempy = np.random.choice(alist)
    if tempx**2 + tempy**2 < (a**2)+1:
        count += 1.
    anotherlist[i] = count/(i+1)*4.

In [78]:

print anotherlist[-1]
plt.plot(anotherlist)

3.0

Out[78]:

[<matplotlib.lines.Line2D at 0xa8b9f58c>]

In [85]:

a = 100
alist = np.arange(0,a+1,1)
andanotherlist = []
for iterations in [10+1,10**2+1,10**3+1,10**4+1,10**5+1,10**6+1]:
    #anotherlist = np.zeros(iterations)
    count = 0.
    #iterations = 100
    for i in xrange(iterations):
        tempx = np.random.choice(alist)
        tempy = np.random.choice(alist)
        if tempx**2 + tempy**2 < (a**2)+1:
            count += 1.
        #anotherlist[i] = count/(i+1)*4.
    andanotherlist.append(count/iterations*4.)

In [86]:

plt.plot(andanotherlist,'o')

Out[86]:

[<matplotlib.lines.Line2D at 0xa8a019ec>]

In [87]:

a = 1000
alist = np.arange(0,a+1,1)
andanotherlist = []
for iterations in [10+1,10**2+1,10**3+1,10**4+1,10**5+1,10**6+1]:
    #anotherlist = np.zeros(iterations)
    count = 0.
    #iterations = 100
    for i in xrange(iterations):
        tempx = np.random.choice(alist)
        tempy = np.random.choice(alist)
        if tempx**2 + tempy**2 < (a**2)+1:
            count += 1.
        #anotherlist[i] = count/(i+1)*4.
    andanotherlist.append(count/iterations*4.)

In [88]:

plt.plot(andanotherlist,'o')

Out[88]:

[<matplotlib.lines.Line2D at 0xa89cffec>]

In []: