Writing a C program to calculate the constant Pi is a great way to delve into the basics of math in programming. In this guide, you will learn a step-by-step explanation on how to calculate Pi using the Leibniz formula for Pi. The Leibniz formula for Pi is represented as Pi = 4*(1/1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 …).
The Leibniz formula for Pi is an infinite series representation of Pi which was discovered by the German mathematician Gottfried Leibniz in the 17th century.
Getting Started: Required Libraries in C
Let’s start off by talking about the libraries we’ll need in this program. We’ll be using the standard math library
[#include <math.h>]
and the library for standard input/output operations
[#include <stdio.h>]
.
- math.h: This library contains various mathematical functions and macros.
- stdio.h: It contains declaration of both standard input and output functions.
Implementing the Leibniz formula for Pi in C
Here’s a basic example of how this implementation can look like. Note that we’ll be using a for loop to iterate over the terms in the series. This code calculates an approximation of Pi up to the ten-thousandth term.
#include
#include
double calculatePi(int term) {
double pi = 0.0;
int sign = 1;
for (int i = 0; i < term; i++) {
pi += (sign * (1.0 / (2.0 * i + 1)));
sign *= -1;
}
pi *= 4.0;
return pi;
}
int main() {
printf("Approximation of Pi: %fn", calculatePi(10000));
return 0;
}
[/code]
Explanation of the Code
In the calculatePi function, we initially set pi as 0.0, and the sign as 1. The function takes in an argument ‘term’, which indicates the number of terms in the series to calculate.
The code then enters a loop, from i = 0 to the given term. In each iteration, we divide 1 by ‘2i+1’, and add or subtract it from our running total of pi, depending on whether i is an even or odd number. This is controlled by the ‘sign’ variable which alternates between 1 and -1 in each iteration, and it why we multiply our total by ‘sign’.
After exiting the loop, we multiply the sum by 4 (as per the Leibniz formula) and return the value. The result is an approximation of Pi.
The ‘main’ function simply prints out the approximation of Pi up to the ten thousandth term by calling the ‘calculatePi’ function.
In conclusion, while calculating Pi using the Leibniz formula might not be the most efficient or accurate, it serves as a great introduction to implementing math in programming, specifically in C.
