### 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)
```

Out[78]:

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]:

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]:

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