I think of "the last two numbers" as a description of recursion. You are effectively saying that the nth Fibonacci number is the sum of the (n-1)th and (n-2)th

I think of "the last two numbers" as a description of recursion. You are effectively saying that the nth Fibonacci number is the sum of the (n-1)th and (n-2)th Fibonacci number, which is the textbook recursive solution. The iterative solution is more like "start with 0 and 1, add them together to get a new number, then add that new number to the larger of the previous two numbers, and do that n times to get the nth Fibonacci number." That works just as well (or better, for computers and large n) as the recursive solution, but it's harder to explain, and it barely even hints at the most notable property of the sequence (that each number is the sum of the previous two numbers).