want to find pi... almost there

[Dan Halen]

What needs changed? It doesn't approximate pi accurately.

#include <iostream>
#include <iomanip>

using namespace std;

int main()
{
	double pi = 1;
	long i;
	long n;
	
	cout << "Enter the value of n: ";
	cin >> n;
	cout << endl;
	
	for (i = 1; i < n; i++)
		{
		if (i % 2 == 0)
			pi = pi + (1.0 / (2.0 * i + 1.0));
		else 
			pi = pi - (1.0 / (2.0 * i + 1.0));
		}
	
		pi = 4 * pi;

	
	cout << endl << "pi = " << pi << endl;
	
	return 0;
}

[tntxtnt]

with n = 1000 it will.

[Dan Halen]

Yes, I see that if the user enters 1000, it works. Does that suggest a change to the code? I don't see the relevance.

[helios]

Iterative approximation algorithms are expected to be relatively inaccurate when they are only allowed to iterate a small number of times. I don't know what kind of answer you're expecting. "Use a different algorithm"?

[Dan Halen]

I know what you mean. It could be that I misunderstood the goal of this assignment (it's for school). "Use a different algorithm" is probably good advice, since understanding the problem is the first step to good programming. I suppose. Thank you.

[tntxtnt]

Leibniz's formula converges slowly. Calculating π to 10 correct decimal places using direct summation of the series requires about 5,000,000,000 terms

http://en.wikipedia.org/wiki/Leibniz_formula_for_pi#Inefficiency

your code is fine. If you want n to be smaller then "Use a different algorithm", as helios said.


you can look up other algorithms here
http://en.wikipedia.org/wiki/Approximations_of_%CF%80#Development_of_efficient_formulae
or http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80

http://upload.wikimedia.org/math/6/d/f/6df9e60b9d00e84e4c625696dfdd620d.png

used the first 21 terms to compute an approximation of pi correct to 11 decimal places as 3.14159265359

this one sounds promising