%
% this code implements formulas from Project 1. Problem 1.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
format long
n=10;
% this implementes formula (1)
x=2;
for i=1:1:n
    x=sqrt(2-sqrt(4-x^2));
end
x=x*(2^n);
%% this line prints the result on the screen
fprintf(1,'Computed: %13.12f Stored %13.12f Error: %13.12f \n \n', x,pi, abs(x-pi));
n=10;
% this implementes formula (1)
y=2;
for i=0:1:n
    y=2*y/sqrt(2+sqrt(4-y^2/4^i));
end
%% this line prints the result on the screen
fprintf(1,'Computed: %13.12f Stored %13.12f Error: %13.12f \n \n', y, pi, abs(y-pi));