[Tutor] getting error while solving a series that estimates the value of pi

[James Reynolds]

On Mon, Jul 18, 2011 at 12:10 PM, surya k <suryak at live.com> wrote:

> Hi,
>
> The problem is to estimate the value of pi using the following series.
>  *1 / pi  = (( 2 * sqrt(2) )/ 9801 )  * SIGMA of k[ (4k)! (1103 + 26390*k)
> / (k!^ 4 ) * 396^(4k)  ]*
> *where k is [0, infinity)*
> * Problem is located at : ThinkPython Book, www.thinkpython.org
>    *Pg 89, Exercise 7.5, Think Python Book. *
> *
> *
> the series should be considered till the last term of the sigma must be <
> 1e-15
> I have written the below code :
>
> *# program estimates the value of pi*
> *# Ramanujan's series... *
> *import math*
> *
> *
> *def fact(n) : # def of factorial function.*
> *    if n > 0 :    *
> *       return n * fact(n-1)*
> *    if n == 0 :*
> *       return 1*
> *
> *
> *k = 0*
> *tot = 0*
> *temp1 = 0*
> *while k >= 0 and temp1 == 0 :*
> *
> *
> *      a = ( 2 * math.sqrt(2) ) / 9801 # first term before sigma *
> *      nu = fact (4*k) * (1103 + (26390*k) )  # numerator of series*
> *      de = pow( fact(k), 4 ) * pow ( 396, 4*k )  # denominator of series*
> *      *
> *      if de / nu > 1e-15 : *
> *            temp = nu / de*
> *            tot = tot + temp*
> *            temp1 = 0 *
> *            k = k + 1 *
> *      elif de / nu  == 1e-15 :*
> *             series = a * tot  *
> *             k = k + 1*
> *             temp1 = 0*
> *      elif de / nu < 1e-15 :*
> *             print series*
> *             temp1 = 1*
>
>
> I am getting the following error : which is completely surprising!
>
> *Traceback (most recent call last):*
> *  File "pi.py", line 30, in <module>*
> *    print series*
> *NameError: name 'series' is not defined*
>
> *
> *
> Thus I have removed name 'series' and replaced with  *a*tot, *
> now I am getting this error
>
> *Traceback (most recent call last):*
> *  File "pi.py", line 30, in <module>*
> *    print 1 / (a * tot)*
> *ZeroDivisionError: float divisio*n
>
>
>
> Thus I changed the first highlighted lines to
>
>  *nu = float (fact (4*k) * (1103 + (26390*k) ) )*
> *      de = float (pow( fact(k), 4 ) * pow ( 396, 4*k )) *
>
>
> now I am getting
>
> * Traceback (most recent call last):*
> *  File "pi.py", line 18, in <module>*
> *    de = float (pow( fact(k), 4 ) * pow ( 396, 4*k ) )*
> *OverflowError: long int too large to convert to float*
>
> *help me out of this problem, how could I fix this*
>
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>


I am getting the following error : which is completely surprising!


You only define "series" when nu/de == XXX. Just don't print series outside
of where it is defined, or print it outside of the while loop if you can be
assured it is defined when the while loop ends.

Even so, you would still end up with the overflow error, because you have de
/ nu and I'm assuming you want nu / de. As an aside, you might want to
consider creating a variable above all the if statements called nude = nu /
de and replace all of the nu / de 's to nude. This way you only divide once
and not (potentially) three times per loop.
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