Fibonacci sequence is a sequence of numbers, where each number is the sum of the 2 previous numbers, except the first two numbers that are 0 and 1.
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
...
The ratio of two sequential Fibonacci numbers, converges to the golden ratio:
φ is the golden ratio = (1+√5) / 2 ≈ 1.61803399
n | Fn |
---|---|
0 | 0 |
1 | 1 |
2 | 1 |
3 | 2 |
4 | 3 |
5 | 5 |
6 | 8 |
7 | 13 |
8 | 21 |
9 | 34 |
10 | 55 |
11 | 89 |
12 | 144 |
13 | 233 |
14 | 377 |
15 | 610 |
16 | 987 |
17 | 1597 |
18 | 2584 |
19 | 4181 |
20 | 6765 |
TBD
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;
}