Application of Computing Coursework

Running head: APPLICATION OF COMPUTING COURSEWORK
APPLICATION OF COMPUTING COURSEWORK
Name of the Student
Name of the University
Author Note

1APPLICATION OF COMPUTING COURSEWORK
Q1:
i) The ratio of Fn/Fn-1 for the first 50 Fibonacci numbers are calculated by the following
MATLAB code.
MATLAB code:
%% Q1 i)
% generating Fibonacci numbers
F(1) = 1; F(2) = 1;
for i=3:50
F(i) = F(i-1) + F(i-2);
end
% computing ratio Fn/Fn-1
n = zeros(1,49);
ratio = zeros(1,49);
for i=2:50
n(i) = i;
ratio(i) = F(i)/F(i-1);
end
%% Q1 ii)
% plotting ratio as a function of n

2APPLICATION OF COMPUTING COURSEWORK
plot(n,ratio)
xlabel('sequence number')
ylabel('Ratio')
title('Ratio as a function of the sequence number')
%% Q1 iii)
i=1;ratio(1)=F(2)/F(1);
g_mean = (1+sqrt(5))/2; % defining golden mean
while (abs(ratio(i)-g_mean)/g_mean)*100 > 0.1 % finding n for which ratio is within 0.1% of
golden mean
i=i+1;
end
sprintf('The smallest value of n=%i for which the ratio is 0.1 percent accurate of golden
mean. The percentage of tolerance is %f',i,(abs(ratio(i)-g_mean)/g_mean)*100)
Output:
fibonacci
ans =
'The smallest value of n=9 for which the ratio is 0.1 percent accurate of golden mean. The
percentage of tolerance is 0.062646'