Thread: cool math homework assignment

Well you can move this to whatever board you want. Anyway I'm taking a course called 'engineering mathematics.' It's kind of the equivalent of a linear algebra course. My professor is an eccentric old lady that is way too smart to teach math to humans.

Our assignment over the weekend was to write in excel a command to evaluate the series for 'e' and 'pi' and to see how many terms in the series it took to get a certain number of decimal places accuracy. She suggested trying a couple of hundred terms, so of course I wrote a program that evaluates PI using 50 million terms. Kind of neat. Here are the results, the series for 'e' converged pretty quickly, not true for PI.

E after 20 terms in the series: 2.718281828459045500000000000000

PI after 1000 terms in series: 3.142593654340044100000000000000

PI after 50000000 terms in series: 3.141592673590250900000000000000

Here's the program for it

Code:

#include <iostream>
#include <fstream>
#include <math.h>

using namespace std;

double	factorial(double	input)
{
	if(input > 0)
		return	input * factorial(input-1);
	else	return	1;
}

double	e_term(double	which_term)
{
	return	1.0 / (factorial(which_term));
}

double	pi_term(double which_term)
{
	int	i_term;
	_asm	
	{
		fld		which_term;
		fistp	i_term;
	}

	double	sgn			=	pow(-1.0,i_term+1);
	double	denom		=	1.0 / ((2.0 * which_term)-1);
	return	4 * sgn * denom;	
}

int main(void)
{
	std::ofstream	fout;
	fout.open("results.txt");
	fout.precision(50);
	cout.precision(50);
	
	double	summation = 0.0;
	for(double	which_term = 0; which_term < 20; ++which_term)
	{
		summation += e_term(which_term);
		fout << summation << "\n";	
	}

	fout << "\n\n\n\n\n\n\n";
	
	
	summation = 0;
	for(which_term = 1; which_term < 1000; ++which_term)
	{
		summation += pi_term(which_term);
	}
	cout << "PI after 1000 terms in series: " << summation << "\n";
	fout << "\nPI after 1000 terms in series: " << summation << "\n\n";

	summation = 0;
	for(which_term = 1; which_term < 50000000; ++which_term)
	{
		summation += pi_term(which_term);
	}

	cout << "PI after 50000000 terms in series: " << summation << "\n";
	fout << "\nPI after 50000000 terms in series: " << summation << "\n\n";
	return	0;
}