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[Melchoire]

This was an exercise in my homework, and I found it pretty interesting/cool so I figured I'd show you guys...

There's some proof out there that states that the probability that two random selected integers being relative prime is 6/π²

You can use this to write a program that estimates π for you:

#include <iostream>
#include <cstdlib>
#include <cmath>
#include <ctime>

#define LIST_SIZE 500000000

using namespace std;

bool rel_prime(int a, int b);

int main()
{
	srand(time(NULL));
	int x, y;
	int acc;
	double pi;
	
	for (int i = 0; i < LIST_SIZE; i++)
	{
		x = rand() % LIST_SIZE + 1;
		y = rand() % LIST_SIZE + 1;
		
		if (rel_prime(x, y))
			acc++;
	}

	pi = sqrt(((double)1) / ((((double)(acc))/((double)(LIST_SIZE))) * 0.1666666)); //could be written better
	
	cout << pi << endl;
	
	return 0;
}

bool rel_prime(int a, int b)
{
	while(true)
	{
		if (!(a %= b)) return b == 1 ;
		if (!(b %= a)) return a == 1 ;
	}
}

It selects a random pair of integers 500,000,000 times to get an accurate estimate. Mine came up with 3.14156...which is pretty darn close =P

I found out you can also derive π from other formulas. For example, picture a circle inscribed inside a square. By choosing a random point inside the square the probability that it will be inside the circle is πr²/4r² = π/4...but that's a more resource intensive method.

So...disucuss cool math stuff =P