I have expressed my strong opinion about using Fibonacci levels for trading in the not so distant past. I did this on my site dedicated primarily to day trading futures, but this opinion applies to trading other instruments as well. I am not going to repeat myself here, so just check out my site for that if interested, which I think you should be. It's in

**this very article**.

Now, what I really want to talk about in this post is how to obtain Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 34, and so on) without rabbits. First, because it only confuses them, the rabbits, and second because you really don't need two rabbits (and of opposite sex) to derive Fibonacci numbers.

You only need one. Meaning number 1. Instead of two numbers (say 0, 1 or 1,1) that would form the start of the Fibonacci sequence to be obtained via the recursive formula, a(n)=a(n-1)+a(n-2). The formula in question, if applied correctly does produce all the known Fibonacci numbers. For instance, a(2)=a(1)+a(0)=1+0=1, a(3)=a(2)+a(1)=1+1=2, a(4)=a(3)+a(2)=2+1=3, etc.

But as I said, we can start just from 1. No need for another number, be it 0 or 1. Having 1 at our disposal, we will be pulling other Fibonacci numbers like rabbits out of a hat (pun intended).

How so? Well, take 1 and add the sum of all the previous numbers, including 1, to it. This sum is 1 in this case, so the next term we obtain this way is 1+1=2. We now have two terms, 1 and 2, and we can repeat the same procedure obtaining 2+(1+2)=5, as our sum is now 1+2. And since we now have three terms, 1, 2, 5, we can use them to obtain the next term: 5+(1+2+5)=13.

What we are getting is 1, 2, 5, 13, ...

Now, if you know the Fibonacci sequence, or saw a piece of it above, you may be feeling a bit uneasy because that really does not very much resemble one.

Well, only partially so. All these numbers are Fibonacci numbers, but it is also true that these numbers are not all Fibonacci numbers, not the complete sequence of them. It's only every other number from this famous sequence.

And that's fine, because if you really want to obtain the full Fibonacci sequence, you can do this quite easily using only the numbers you have obtained so far and all those that you can continue obtaining in the way outlined above.

You simply subtract the numbers obtained, so 2-1=1 and it goes between 1 and 2, then 5-2=3 and it goes between 2 and 5, and 13-5=8 that goes, obviously, between 5 and 13.

In other words, we can obtain the entire Fibonacci sequence starting just from a single number, 1.

But the sequence of every other Fibonacci number is even easier to obtain starting just from 1 and hence perhaps it is even more fundamental in some way.

Incidentally, I have not seen this kind of derivation before, although I am rather familiar with the Fibonacci literature, but perhaps someone else has come up with it before me, so I will abstain from claiming any priority. Not to mention that this is, at the very best, just a piece of recreational mathematics.