<pre><script>
var x = 1;
var y = 1;
for(i=1; i<=100; i++) {
  document.writeln(i+' : '+(y/x));
  var z = x+y;
  if(y/x==z/y) break;
  else { x = y; y = z; }
}
</script></pre>

40 : 1.618033988749895

<pre><script>
var x = 1.618;
for(i=1; i<=100; i++) {
  document.writeln(i+' : '+x);
  var y = 1+1/x;
  if(x==y) break;
  else x = y;
}
</script></pre>

28 : 1.618033988749895

<pre><script>
var x = □;
for(i=1; i<=100; i++) {
  document.writeln(i+' : '+x);
  var y = (x*x+2)/(2*x);
  if(x==y) break;
  else x = y;
}
</script></pre>

6 : 1.414213562373095

8 : 1.414213562373095