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Jan 2, 2019 at 22:31 comment added Somos Yes, but isn't $\,x^n\,$ defined recursively? You still don't avoid recursion. Also, the golden ratio is not rational. If you define $\,\phi\,$ as the positive root of $\,x^2=x+1\,$ then $\,\phi^n = F_{n-1}+F_n\phi\,$ so $\,\phi^n\,$ is defined by $\,F_n.$
Jul 17, 2012 at 15:40 history answered dab CC BY-SA 3.0