Phibonacci - Relation between Phi and Fibonacci
JavaScript (ES7),  77 75 69  67 bytes

n=&gt;(g=p=&gt;--n&gt;1?g(q,q+=p):(1+5**.5)/2*(m*=10)^q/p*m?0:1+g(p))(q=m=1)

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n =&gt; (            // main function, taking n
  g = p =&gt;        // g is a recursive function taking p which, along with q,
                  // is used to compute the Fibonacci sequence
  --n &gt; 1 ?       // decrement n; if it's still greater than 1:
    g(q, q += p)  //   do a recursive call with (p, q) = (q, q + p)
  :               // else:
    (1 + 5 ** .5) //   compute the golden ratio
    / 2           //
    * (m *= 10)   //   multiply m by 10 and multiply the golden ratio by m
    ^             //   xor (forces the decimal places to be discarded)
    q / p         //   compute q / p (last Fibonacci term / penultimate one)
    * m           //   multiply by m
    ?             //   if the above values are not equal:
      0           //     stop
    :             //   else:
      1 + g(p)    //     increment the final result and do a recursive call
)(q = m = 1)      // initial call to g with p = q = m = 1