[radicality]

Where are you getting at with the the t(n)? As you said, the golden ratio is defined as the limit of f(n+1)/f(n), and yes, with this implementation (because f ~ t) t(n+1)/t(n) also converges to the golden ratio, but... so what, why not just use f ?

[NAFV_P]

It's been done before. Calculating the golden ratio using your method provides insights into the world of mathematics. My method provides insights into the world of programming.