Find The Value Of Pi

i need to find the value of pi using below pattern, pi = 4/1-4/3+4/5-4/7+4/9 i have been able to find the denominator and change the sign but i am having trouble using it in the w

Solution 1:

You just forgot to update prev, so the loop never terminates. I also put in an abs in case the difference is negative.

def pi(error):
    prev =1current=4
    i =1
    while abs(current- prev) > error:
        d =2.0* i +1
        sign = (-1)**i
        prev =currentcurrent=current+ sign *4/ d
        i = i +1returncurrent

I tried pi(0.001) with this code and got the answer 3.1420924036835256. Note that if you try something like pi(0.000000001) the console will freeze for a while because it will take a long time for the loop to terminate.

Solution 2:

As an alternative you could use itertools:

itertools.count(1, 2)    # generates the sequence 1, 3, 5, 7, ...
itertools.cycle([1, -1]) # generates the sequence 1, -1, 1, -1, ...

So you could do, and this generates the right values (note: moved the 4* outside of the loop to get the correct answers):

from itertools import count, cycle #, izip - if Py2defpi(error):
    p = 0for sign, d inzip(cycle([1,-1]), count(1, 2)):  # izip for Py2
        n = sign/d
        p += n
        ifabs(n) < error:
            breakreturn4*p

>>> pi(0.01)
3.1611986129870506>>> pi(0.0000001)
3.1415928535897395

Or using a generator:

from itertools import count, cycle, takewhile #, izip - if Py2defpi_series():
    for sign, d inzip(cycle([1,-1]), count(1, 2)):  # izip - if Py2yield sign/d

defpi(error):
    return4*sum(takewhile(lambda x: abs(x) > error, pi_series()))

But this doesn't add the last term (need takeuntil)