In [6]:

    

def print_n(s, n):
    while n > 0:
        print(s)
        n -= 1


    

In [7]:

    

print_n('hi there', 3)


    

    




hi there
hi there
hi there

In [51]:

    

def square_root(a):
    epsilon = 1e-7
    x = a / 2.
    while True:
        y = (x + a/x) / 2
        if abs(x - y) < epsilon:
            break
        x = y
    return x


    

In [40]:

    

square_root(144)


    

    
Out[40]:





12.000000010666378

In [49]:

    

import math
def test_square_root(a_lo, a_hi):
    for a in range(a_lo, a_hi+1):
        actual = math.sqrt(a)
        approx = square_root(a)
        error = abs(actual - approx)
        print "{}\t{}\t{}\t{}".format(a, actual, approx, error)


    

In [52]:

    

test_square_root(1, 9)


    

    




1	1.0	1.00000004646	4.64611473738e-08
2	1.41421356237	1.41421356237	1.59472435257e-12
3	1.73205080757	1.73205081001	2.44585018905e-09
4	2.0	2.0	0.0
5	2.2360679775	2.23606797792	4.16013890003e-10
6	2.44948974278	2.44948979592	5.31351895816e-08
7	2.64575131106	2.64575131106	1.02584607475e-13
8	2.82842712475	2.82842712475	3.18944870514e-12
9	3.0	3.00000000004	3.9321434997e-11

In [1]:

    

def eval_loop():
    while True:
        user_input = raw_input(">")
        if user_input == "done":
            break
        print eval(user_input)


    

In [5]:

    

eval_loop()


    

    




>324 * 89324
28940976
>done

In [15]:

    

import math

def estimate_pi():
    k = 0.
    term_min = 1e-15
    term = term_min + 1 # need to get in to the loop
    term_sum = 0
    const_factor = 2 * math.sqrt(2) / 9801
    while abs(term) > term_min:
        numer = math.factorial(4*k) * (1103 + 26390*k)
        denom = math.factorial(k)**4 * 396**(4*k)
        term = numer / denom
        term_sum += term
        k += 1
        print term

    return 1 / (const_factor * term_sum)


    

In [20]:

    

estimate_pi()


    

    
Out[20]:





3.141592653589793

In [21]:

    

estimate_pi() - math.pi


    

    
Out[21]:





0.0

In [17]:

    

import math

def estimate_pi():
    k = 0.
    term_sum = 0
    const_factor = 2 * math.sqrt(2) / 9801
    while True:
        numer = math.factorial(4*k) * (1103 + 26390*k)
        denom = math.factorial(k)**4 * 396**(4*k)
        term = numer / denom
        term_sum += term
        if abs(term) < 1e-15: break
        k += 1

    return 1 / (const_factor * term_sum)


    

In [22]:

    

estimate_pi()


    

    
Out[22]:





3.141592653589793

In [23]:

    

math.pi - estimate_pi()


    

    
Out[23]:





0.0