Madhava approximation of pi

I am trying to approximate the value of pi using the equation Madahava of Sangamagrama used.

The code that I have so far is:

function [ output_args ] = madhavapi(m)
%This function will takes N as input and returns an approximation for pi.
k=[0 1 2 3 4]

1./(-3).k
[1/(-3)^0/(-3)^1/(-3)^2;
1./(2.*k-1)
1./sum*12

end

I am not sure how to conclude this code. When I try to execute the above code, I do not get any answer.

[Marc]

Wasn't Madahava Sangamagrama a wizard in The Lord of the Rings?

[KayLynn]

I wouldnt know that. Are you able to help me with the last statement or so of this code. I am basically seeking help with the way to end this code in order to get an output that results in approximating pi.

[Walter Roberson]

You did not assign anything to "output_args"

"sum" is a function, not a variable.

You do not use "m" anywhere in your function.

The expression

1./(-3).k

is not valid. There is no "." operator in MATLAB.

Answer 1

[sixwwwwww]

Dear Kaylynn, here is the function which approximates value of pi using Madahava Sangamagrama equation:

function [ output_args ] = madhavapi(m)
k = 0:m;
output_args = 4 * sum((-1).^k ./ (2 * k + 1));
end

I hope it helps. Good luck!

[KayLynn]

I want to take an input N and return the approximate value of pi. For example if my N equals 2, I should get an output of 3.152 right?

[sixwwwwww]

To take 'N' change the first two lines of above code as:

function [ output_args ] = madhavapi(N)
k = 0:N;

and here is the link which describes Madahava Sangamagrama equation: http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80. So according to this equation if you put N = 2 then you will get output 3.46666666666667. As you will increase the value of N then output will come close to well known value of pi: 3.1415...