Archimedes method to compute pi

pi.py

p = 4.0/(2**0.5)
P=4

def one_round(t):
    p,P = t
    P2 = 2*p*P/(p+P)
    p2 = (p*P2)**0.5
    return p2,P2

s = '%3.10f  %3.10f'
print '%2d' % 2, s % (p,P)

for i in range(3,20):
    p,P = one_round((p,P))
    print '%2d' % i, s % (p,P)

```
> python pi.py
 2 2.8284271247  4.0000000000
 3 3.0614674589  3.3137084990
 4 3.1214451523  3.1825978781
 5 3.1365484905  3.1517249074
 6 3.1403311570  3.1441183852
 7 3.1412772509  3.1422236299
 8 3.1415138011  3.1417503692
 9 3.1415729404  3.1416320807
10 3.1415877253  3.1416025103
11 3.1415914215  3.1415951177
12 3.1415923456  3.1415932696
13 3.1415925766  3.1415928076
14 3.1415926343  3.1415926921
15 3.1415926488  3.1415926632
16 3.1415926524  3.1415926560
17 3.1415926533  3.1415926542
18 3.1415926535  3.1415926537
19 3.1415926536  3.1415926536
> 
```