Print pi to a number of decimal places

Question

One of the challenges on w3resources is to print pi to \'n\' decimal places. Here is my code:

from math import pi

fraser = str(pi)

length_of_pi = []

numbe         


        

Answer 1

Your solution appears to be looping over the wrong thing:

for number_of_places in fraser:

For 9 places, this turns out be something like:

for "9" in "3.141592653589793":

Which loops three times, one for each "9" found in the string. We can fix your code:

from math import pi

fraser = str(pi)

length_of_pi = []

number_of_places = int(raw_input("Enter the number of decimal places you want: "))

for places in range(number_of_places + 1):  # +1 for decimal point
    length_of_pi.append(str(fraser[places]))

print "".join(length_of_pi)

But this still limits n to be less than the len(str(math.pi)), less than 15 in Python 2. Given a serious n, it breaks:

> python test.py
Enter the number of decimal places you want to see: 100
Traceback (most recent call last):
  File "test.py", line 10, in 
    length_of_pi.append(str(fraser[places]))
IndexError: string index out of range
> 

To do better, we have to calculate PI ourselves -- using a series evaluation is one approach:

# Rewrite of Henrik Johansson's (Henrik.Johansson@Nexus.Comm.SE)
# pi.c example from his bignum package for Python 3
#
# Terms based on Gauss' refinement of Machin's formula:
#
# arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...

from decimal import Decimal, getcontext

TERMS = [(12, 18), (8, 57), (-5, 239)]  # ala Gauss

def arctan(talj, kvot):

    """Compute arctangent using a series approximation"""

    summation = 0

    talj *= product

    qfactor = 1

    while talj:
        talj //= kvot
        summation += (talj // qfactor)
        qfactor += 2

    return summation

number_of_places = int(input("Enter the number of decimal places you want: "))
getcontext().prec = number_of_places
product = 10 ** number_of_places

result = 0

for multiplier, denominator in TERMS:
    denominator = Decimal(denominator)
    result += arctan(- denominator * multiplier, - (denominator ** 2))

result *= 4  # pi == atan(1) * 4
string = str(result)

# 3.14159265358979E+15 => 3.14159265358979
print(string[0:string.index("E")])

Now we can take on a large value of n:

> python3 test2.py
Enter the number of decimal places you want: 100
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067
>