Calculating Pi

[bridgster]

For class we need to write a program that takes in an input (n) that determines the number of terms in the approximation of the value of pi and outputs the approximation. The program also needs a for loop to calculate this until the user wants to quit using the program.

The formula for pi that was given to us was.

pi = 4 [ 1 - 1/3 + 1/5 - 1/7 + 1/9 ... +((-1)^n)/(2n+1) ]

The main problem we have is, how to write the formula into the program. We are lost and will take any advice or help at this point, thanks in advance!

[keskiverto]

You have the formula right there: every successive n adds 4*((-1)^n)/(2n+1).

That is the theory. Finding the most numerically accurate way to compute that with or without floating point numbers is an another challenge.

[bridgster]

Thanks, might have to take a zero on this one.. we are lost!

[Codeez]

You could check out some other peoples examples:

http://www.cplusplus.com/search.do?q=+Calculating+Pi+
https://www.google.co.uk/#q=+Calculating+Pi+C%2B%2B

[giblit]

You should be able to do it pretty easily with a for loop


Basically something like this

double pi( int n )
{
     double pi = 4.0 , decimal = 1.0;
     while( n > 2 )
    {
        decimal -= ( 1.0 / ( 2.0 * n + 1 ) );
        --n;
        decimal += ( 1.0 / ( 2.0 * n + 1 ) );
        --n;
    }
    if( n > 0 )
        decimal -= ( 1.0 / ( 2.0 * n + 1 ) );
    return( pi * decimla );
}

I could be wrong though but it looks to me like the formula is

4 * (1 / 1 + 2n ) The inside part would be all the fractions added up ex 1 / 1 - 1 / 3 + 1 / 5 - 1/7

So if n was 3 then it would be ( I gave it the 0 by default so I start at 1 and go to 3 ) When I say I gave it 0 by default I mean I initialized it to 1
4 * ( -1/7 + 1/5 - 1/3 + 1/1 ) = 4 * ( 0.72380952380952380952380952380952 ) = 2.8952380952380952380952380952381

Am I misunderstanding the formula you provided?

Also yes I did do it in reverse order

But basically if n is even say for example 4

That would mean
1 - + - +

And I started with -

And an odd would end in a -
so lets look at 3
1 - + -