fibonacci

Fibonacci number

Usage

F = fibonacci(N)

• N should be an array of non-negative real integers, not equal to Inf nor NaN.
• F is an array of the same size of N. Each element in F is the Fibonacci number of the corresponding element in N.
• F is empty if N is empty.
• 💡 When an element in N is large, the Fibonacci number is a double-precision floating-point approximation.

Example

• The first 11 Fibonacci numbers.

Input

fibonacci(0:10)

Output

ans =
Columns 1 through 5:
 0.000   1.000   1.000   2.000   3.000
Columns 6 through 10:
 5.000   8.000   13.00   21.00   34.00
Column 11:
 55.00

• $F_{n} / F_{n-1}$ approximates the Golden Ratio for a large $n$.

Input

fibonacci(100) / fibonacci(99)

Output

ans =
 1.61803398874989

• Convergence of $F_{n} / F_{n-1}$ to the Golden Ratio.

Input

gs=fibonacci(1:30)./fibonacci(0:29);
plot(gs,'-p','MarkerFaceColor','r')
xlabel('n')
title('Approximation of Golden Ratio')

Output