Why are Fibonacci numbers significant in computer science?

Question

Fibonacci numbers have become a popular introduction to recursion for Computer Science students and there\'s a strong argument that they persist within nature. For these reasons

Answer 1

Greatest Common Divisor is another magic; see this for too many magics. But Fibonacci numbers are easy to calculate; also it has a specific name. For example, natural numbers 1,2,3,4,5 have too many logic; all primes are within them; sum of 1..n is computable, each one can produce with other ones, ... but no one take care about them :)

One important thing I forgot about it is Golden Ratio, which has very important impact in real life (for example you like wide monitors :)