The guy stopped at Binet's formula. Could have gone into series polynomials[1] and linear algebra encoding M = ((1 1) (1 0)), Fib(n) = M^n [2].

I was just skimming through http://www.wiley.com/WileyCDA/WileyTitle/productCd-047063157... (Fibonacci and Catalan numbers)

[1] https://en.wikipedia.org/wiki/Golden_ratio#Mathematics [2] https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form