# fibonacci

Fibonacci number

### F = fibonacci(N)

• N should be an array of non-negative real integers.
• 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.

Note

When an element in N is large, it's Fibonacci number given by F is a double-precision floating-point approximation.

Example 1: The first 11 Fibonacci numbers.

fibonacci(0:10)

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


Example 2: $F_{n} / F_{n-1}$ approximates the Golden Ratio for a large $n$.

fibonacci(100) / fibonacci(99)

ans =
1.61803398874989


Example 3: Convergence of $F_{n} / F_{n-1}$ to the Golden Ratio.

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