Fibonacci and Golden Ratio
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One of the ways to compute the golden ration
4 个评论
Jan
2011-4-4
@Ashley: Don't give up: As soon as you edit the question and add any details - and a question! - you will get meaningful answers.
Khan Muhammad Babar
2020-12-17
Is there any way to quantify the Golden mean of Image in MATLAB. Please help.
回答(5 个)
Clemens
2011-8-17
Actually the Golden Ratio is exactly:
( 1 + sqrt(5) ) / 2
so no need for iteration. Proof is easy through z-transform.
2 个评论
Walter Roberson
2011-8-17
But that gets back to my original answer, "The Golden Ratio is an irrational number, and thus an infinite number. It is not possible to compute its decimal expansion in a finite amount of time."
Jan
2011-8-17
Fortunately the universe is finite. Therefore I do not believe, that an infinite number will match into it. While there is a minimal Planck length and a minimal Plank time, I propose a Planck eps for irrational numbers. According to Rupert Sheldrake, I claim that PI has as many numbers as has been calculated already. And after reading http://scientopia.org/blogs/goodmath/2010/12/08/really-is-wrong/ I'm not sure at all anymore about this fuzzy digits stuff.
Walter Roberson
2011-4-4
The Golden Ratio is an irrational number, and thus an infinite number. It is not possible to compute its decimal expansion in a finite amount of time.
8 个评论
Sean de Wolski
2011-4-4
Soya sausages? That's like one term in the Taylor-series expansion of sausages.
Walter Roberson
2011-8-17
Jan, Soya Beans used for the production of soya products are the dried fruit of the soya plant, and thus were not covered by the Veggi-Toolbox in R2011a (which, I understand, is still withheld from production due to legal battles over whether Tomatoes are fruits or vegetables....)
Walter Roberson
2011-4-4
Let F(t) be Fibonacci number #t. Then
y = 100; %initial guess
x = (F(t+2) * y + F(t+1)) / (F(t+1) * y + F(t));
while x ~= y;
y = x;
x = (F(t+2) * y + F(t+1)) / (F(t+1) * y + F(t));
end
When the loop finishes (no more than a few centuries later, I'm sure), x and y will be the Golden ratio.
3 个评论
Kishore
2023-7-8
fib=[0 1];
i=3;
while(i<=21)
fib(i)=fib(i-1)+fib(i-2);
gr=fib(i)/fib(i-1)
i=i+1;
end
disp(fib)
0 个评论
Guna
2024-4-16
% Function to calculate Fibonacci sequence up to a certain number of terms
function fib_sequence = fibonacci(n)
fib_sequence = zeros(1, n);
fib_sequence(1) = 0;
fib_sequence(2) = 1;
for i = 3:n
fib_sequence(i) = fib_sequence(i-1) + fib_sequence(i-2);
end
end
% Calculate the golden ratio using Fibonacci sequence
n = 20; % Number of Fibonacci terms to generate
fib_seq = fibonacci(n);
% Calculate the ratio of consecutive Fibonacci numbers
golden_ratio_approximations = fib_seq(3:end) ./ fib_seq(2:end-1);
% Display the approximations of the golden ratio
disp('Approximations of the golden ratio using Fibonacci sequence:');
disp(golden_ratio_approximations);
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