Fibonacci numbers

Fibonacci numbers is a sequence of numbers that begins with the digits 0 and 1, and each subsequent value is the sum of the two previous ones.

Fibonacci Sequence Formula

For example:

• F₀ = 0
• F₁ = 1
• F₂ = F₁+F₀ = 1+0 = 1
• F₃ = F₂+F₁ = 1+1 = 2
• F₄ = F₃+F₂ = 2+1 = 3
• F₅ = F₄+F₃ = 3+2 = 5

Golden Section

The ratio of two consecutive Fibonacci numbers converges to the golden ratio:

where φ is the golden ratio = (1 + √5) / 2 ≈ 1,61803399

Most often, this value is rounded up to 1,618 (or 1,62). And in rounded percentages, the proportion looks like this: 62% and 38%.

Fibonacci Sequence Table

C-code (C-code) functions

double Fibonacci(unsigned int n) {     double f_n =n;     double f_n1=0.0;     double f_n2=1.0;       if( n > 1 ) {         for(int k=2; k<=n; k++) {             f_n  = f_n1 + f_n2;             f_n2 = f_n1;             f_n1 = f_n;         }     }     return f_n; }