MATLAB Answers

The Fibonacci Sequence and Golden Ratio.

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Jose Grimaldo
Jose Grimaldo on 24 Mar 2020 at 21:43
Answered: Rashed Mohammed on 27 Mar 2020 at 7:53
Im having trouble calculating the Golden Ratios until the desired accuracy is reached
% Code
Fibonacci Sequence
F=[1 1 2 3 5 8 13 21 34 55]
DA=input('How many decimals of accuracy would you like to calculate the Golden Ratio to: ');
G=round(((1+sqrt(5))/2),DA);
GR(1)=0;
for index=2:N % N, is equal to 10
GR(index)=F(index)/F(index-1);
index=index+1;
if round(GR,DA)==G
end
end

  2 Comments

Geoff Hayes
Geoff Hayes on 24 Mar 2020 at 22:00
Jose - careful with code like
round(GR,DA)==G
because GR is an array whereas DA and G are scalars. Do you really mean to compare (or whatever) the array GR with DA and G? Or do you just want to consider the last element of GR? Also, you use == (generally) when comparing integers and not when using doubles (due to floating point precision, etc.) and so instead would use some sort of tolerance test to see if two doubles (or floats) are "close enough". This might be something like
abs(x - y) < eps
to check to see if the difference between the two numbers is small enough (less than eps) so that x and y can be considered equal. You will probably need to do something here with the last element calculated in GR and G.
David Hill
David Hill on 24 Mar 2020 at 22:11
I believe that you need to calculate the Fibonacci number as you go and should not use a lookup table. I suggest you use a while loop looking at the difference of the last two Golden ratios calculated to determine if the accuracy requirement is met. If accuracy greater than floating point is required, then that is another problem. Try something like:
F(1:2)=1;
GR(1:2)=[0,1]
c=3;
while abs(GR(end)-GR(end-1))>10^-DA
F(c)=F(c-1)+F(c-2);
GR(c)=F(c)/F(c-1);
c=c+1;
end

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Accepted Answer

Rashed Mohammed
Rashed Mohammed on 27 Mar 2020 at 7:53
Hi Jose,
I understand that you would like to calculate Golden Ratio’s until a desired accuracy is reached. There are three problems I can notice from your code.
  1. You have a fixed number of Fibonacci numbers on which you are calculating golden ratios. The desired accuracy may or may not be present in the calculated golden ratios since it is a limited set. As David mentioned you need to calculate the Fibonacci numbers as you go.
  2. The code round (GR,DA) == G gives you a logical vector and if block only executes when all the values in logical vector are 1. Hence even when you reach a desired accuracy the if block may or may not execute depending on previous values of GR.
  3. Whenever you are testing for accuracy, it is recommended to check for closeness of value instead of them being equal as suggested by both Geoff and David.
You can try the following code.
F(1:2) = 1;
DA = input('How many decimals of accuracy would you like to calculate the Golden Ratio to: ');
G = ((1+sqrt(5))/2);
GR = 1;
index = 3;
while abs(G-GR) > 10^-DA
F(index) = F(index-1)+F(index-2);
GR = F(index)/F(index-1);
index = index + 1;
end

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