archimedes.py

import sys, math
try:
    r = int(sys.argv[1])
    R = range(r)
except:
    print('enter the number of cycles')
    sys.exit()

def f(sin,cos):
    cot = cos/sin
    csc = 1/sin
    while True:
        yield 1/csc
        cot = cot + csc
        csc = math.sqrt(1 + cot**2)

sq = math.sqrt(3)
g = f(0.5,sq/2)

n = 6

for i in R:
    print('%2d:  %3.14f' % (i+1, n*next(g)))
    n *= 2

print('pi: ', math.pi)

'''
> p3 archimedes.py 24
 1:  3.00000000000000
 2:  3.10582854123025
 3:  3.13262861328124
 4:  3.13935020304687
 5:  3.14103195089051
 6:  3.14145247228546
 7:  3.14155760791186
 8:  3.14158389214832
 9:  3.14159046322805
10:  3.14159210599927
11:  3.14159251669216
12:  3.14159261936538
13:  3.14159264503369
14:  3.14159265145077
15:  3.14159265305504
16:  3.14159265345610
17:  3.14159265355637
18:  3.14159265358144
19:  3.14159265358770
20:  3.14159265358927
21:  3.14159265358966
22:  3.14159265358976
23:  3.14159265358979
24:  3.14159265358979
pi:  3.141592653589793
>
'''