Why does calculating pi using a loop not work correctly?

Question

We got an assignment where we have to calculate the value of pi using the formula pi/4=1-1/3+1/5-1/7+1/9-1/11...(using 100 terms) but it doesn't seem to run the while-loop for some reason. We're students who have no prior experience of writing code and are just starting.

double pi = 1;
int count = 0;
int n = 3;

while (count < 100) {
    if ((count&1) == 0) {  
        pi = pi - 1 / n;
    } else {
        pi = pi + 1 / n;
    }
    n = n + 2;
    count++;
}
out.print(pi*4);   //why is it printing out pi=1?????

1/n will be always 0 as you are divide int by int and result is int also — Natalia
– Natalia, Commented Sep 3, 2016 at 14:23
consider using += or -= operators to increment/decrement your variable — Nicolas Filotto
– Nicolas Filotto, Commented Sep 3, 2016 at 14:31

progyammer · Accepted Answer · 2016-09-03 14:31:32Z

7

The problem is you do not type cast. pi is double but 1/n returns int, since both the denominator and numerator are integers. This happens in JAVA. Basically, every time, 1/n which is actually fractional, returns 0 (int) for every n > 1 due to lack of type casting. So pi's value is always 1 and in the end pi*4 displays 4.0. So you have to convert (cast) the numerator or the denominator as fractional (double) to make 1/n fractional.

To solve the problem, change the statements

pi = pi + 1 / n;
pi = pi - 1 / n;

to

pi = pi + 1.0 / (double) n;
pi = pi - 1.0 / (double) n;

This displays the output as 3.1514934010709914.

edited Sep 3, 2016 at 14:31

answered Sep 3, 2016 at 14:22

progyammer

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3 Comments

Nicolas Filotto Over a year ago

no need to cast n as double since 1.0 is a double, the result will be a double

progyammer Over a year ago

@NicolasFilotto yes. But that's just to show the OP what exactly I'm trying to do. Plus it helps understand better.

user6790886 Over a year ago

thank you. we solved it by declaring n as a double though. at the time we were still learning about int and double.

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