The other day, as an excuse to play around with custom iterators, I created some completely over-engineered code to calculate the Fibonacci sequences. But surely such a simple function can be implemented in fewer than my 15 lines? (Rick Wicklin, who writes the SAS blog *The Do Loop*, thinks so too.) We could use such a function to more easily show that the ratio of successive Fibonacci numbers tends to the Golden Ratio.

Barry Rowlingson suggests this function to calculate the ratio between the nth and n+1th Fibonacci number:

> fibrat=function(n){a=1;b=1;for(i in 1:n){t=b;b=a;a=a+t};return(a/b)}
> fibrat(99)
[1] 1.618034

A slight tweak to Barry's code yields a function to calculate the Nth Fibonacci number in 55 characters:

fib=function(n){a=0;b=1;for(i in 1:n){t=b;b=a;a=a+t};a}

I can do it in 1 fewer characters with the closed-form solution:

fib=function(n){g=(1+sqrt(5))/2;(g^n-(1-g)^n)/sqrt(5)}

But given that this equation is written in terms of the Golden Ratio, using it to *derive* the Golden Ratio pretty much defeats the purpose.

jebyrnes suggests another means of calculating the Golden Ratio from fibonacci numbers, this time using the sapply function:

> fv<-c()
> sapply(1:20, function(i) if(i<3){fv[i] <<- 1}else
+ {fv[i]<<-fv[i-1]+fv[i-2]})[-1]/fv[-length(fv)]
[1] 1.000000 2.000000 1.500000 1.666667 1.600000 1.625000 1.615385 1.619048
[9] 1.617647 1.618182 1.617978 1.618056 1.618026 1.618037 1.618033 1.618034
[17] 1.618034 1.618034 1.618034

jebyrnes also pointed me to this page of Fibonacci 1-liners in many languages including C, Java and Python. Unless I'm mistaken, R is now very close to holding the record for shortest 1-liner.

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