How to write a Matlab program to calculate pi using Gregory/Leibnitz series

A sample run of the program:

Enter number of terms to calculate (1000 or more): 999

You entered: 999, which is too few terms

The number of terms is set to 1000

pi calculated by Gregory/Leibnitz at end of loop: 3.1405926538

Matlab value of pi: 3.1415926536

Difference with Matlab value of pi at end of loop: -0.0009999997

Graph of difference from Matlab pi for first 100 terms is in Figure 1

Program ended

How do I get started with this program??

Answer 1

[ag]

Hi Devin,

The below code demonstrates how to calculate an approximation of (\pi) using the Gregory-Leibniz series and compare it with MATLAB's built-in value of (\pi). It also demonstrates how to create a graph the difference from MATLAB's (\pi) for the first 100 terms:

% Prompt the user to enter the number of terms
% numTerms = input('Enter number of terms to calculate (1000 or more): ');
numTerms = 1001;

% Check if the entered terms are less than 1000
if numTerms < 1000
    fprintf('You entered: %d, which is too few terms\n', numTerms);
    numTerms = 1000;
    fprintf('The number of terms is set to 1000\n');
end

% Initialize variables
piApprox = 0;
differences = zeros(1, min(100, numTerms)); % Store differences for first 100 terms

% Calculate pi using the Gregory-Leibniz series
for k = 0:numTerms-1
    piApprox = piApprox + ((-1)^k) / (2*k + 1);
    
    % Store the difference for the first 100 terms
    if k < 100
        differences(k+1) = abs(piApprox * 4 - pi);
    end
end

% Multiply by 4 to get the approximation of pi
piApprox = piApprox * 4;

% Display the results
fprintf('pi calculated by Gregory/Leibnitz at end of loop: %.10f\n', piApprox);

pi calculated by Gregory/Leibnitz at end of loop: 3.1425916543

fprintf('Matlab value of pi: %.10f\n', pi);

Matlab value of pi: 3.1415926536

fprintf('Difference with Matlab value of pi at end of loop: %.10f\n', piApprox - pi);

Difference with Matlab value of pi at end of loop: 0.0009990007

% Plot the difference for the first 100 terms
figure;
plot(1:100, differences, 'b-', 'LineWidth', 2);
xlabel('Number of Terms');
ylabel('Difference from MATLAB pi');
title('Graph of difference from MATLAB pi for first 100 terms');
grid on;

fprintf('Graph of difference from Matlab pi for first 100 terms is in Figure 1\n');

Graph of difference from Matlab pi for first 100 terms is in Figure 1

fprintf('Program ended\n');

Program ended

Hope this helps!

[Walter Roberson]

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