Intro to Fibonacci

What Is Fibonacci?

The year is c.1250. You’re in Pisa, Italy. You know, with the “Leaning Tower of …”. “filius Bonacci”, meaning the “son of Bonacci”, becomes Fibonacci.

He's a mathematician. And he's credited with discovering the number 0.

Or at least making it prominently known.

His legacy is derived from the following question –

- the question of the day was,

“You start with one pair of rabbits. It takes one month for them to mature before they can breed and create another pair of rabbits.

Then, this second pair of rabbits take a month to mature before creating another pair.

But, the original pair has a second pair. And each month, another pair.

Each new pair of rabbits takes a month to mature before they can breed another pair. Every month thereafter, every pair has one more pair. They take a month mature and so on and so forth.”

The question is,

at the end of 12 months,

‘how many pairs of rabbits are there’?.

These intellectuals have gotta get a life. They have way too much time on their hands to be coming up with questions like this. But, they did.

Of course you can draw a chart like a tree chart and create 12 rows.

Fill in each pair and their maturing and breeding.

For 12 months. Count them up. And there’s your answer.

But there is a mathematical way.

It is the “Fibonacci” number series.

It goes like this –

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 etc., etc.

Start with 1 pair. - 1

There is only 1 pair after a 2nd month. - 1

But, then the 3rd month they have another pair of rabbits. - 2

The 4th month the original pair breeds another pair,

but the 2nd pair is still maturing. They don’t have another pair yet. – 3

And so on …

This works out to be:

each number is derived by adding the previous 2 numbers.

One and one is 2. 1 and 2 is 3.

Two and 3 is 5. 3 and 5 is 8.

5 and 8 is 13. 8 and 13 is 21.

And so forth.

The 12th number, or ‘months’ down the line, is 144.

Oddly enough, the square of 12.

So, the answer is, 144 pairs of rabbits.

This number series has a ‘bazillion’ interesting facets to it.

If you take any 2 numbers side by side, and divide the first one by the 2nd,

the answer is approximately always ‘0.618’ +/-.

You may get .61756, or .618.4, but, you get the idea.

The ‘further out’ you go, the closer you will always get to .618.

Example 5 / 8 = .625 , ~= .618 – rounded off, .62.

55 / 89 is .6179

If you do the opposite - divide 89 by 55, the answer is, 1.618.

If you divide 34 by 21, the answer is 1.619.

Now, if you take every other number, divide the first one by 2 down the line,

the answer is 0.382.

For example 5 / 13 = .385 . ~= .382 .

13 / 34 = .382 .

Take every 4th one, divide the first one by the 3 down.

Example, 5 divided by 21 = .237

21 divided by 89 = .237.

Okay. Take .618, add it to .382, the answer is 1.

If you take .237, and add .382 the answer is .618

If you square .618, the answers .382 .

There are more interesting facets to the Fibonacci number series.

Google it up.

If you’re a math geek.

But I’ll stop her. I’ve probably go on too far already.


This number series has a Greek symbol, phi, ɸ .

The really interesting thing about this number series is, it defines the cosmos mathematically.

For example, the spiral arms of galaxies, are based on this number series – the Golden Spiral.

The seeds of the sunflower are arranged in Fibonacci spirals. 21 spirals going in one direction, 34 going in the opposite direction.

The arrangement of seeds on a pine cone are in the shape of that spiral.

An awful lot of flowers have either 3 or 5 petals.

The “Golden Ratio” is based on .618 plus .382 being equal to 1.

The Parthenon is architecturally based on the Golden ratio.

The pyramids have relationships with the Golden Ratio.

The human body.

It's got 5 appendages. Counting the head, 2 arms, 2 legs.

The arms and legs are broken into 3 sections.

At the end, the hands (and feet) are broken into 5 fingers (toes).

Each of these is broken into 3 joints.

Our DNA is a double Helix with mathematics of the “Golden Ratio”.

It goes on.

Last week I wrote a very brief intro to Elliott Wave Theory.

One tenet said, “the markets movements up and down,

i.e. – progress and regress, - were based on ‘… mass human nature …’ “.

So, this “mass human nature” is based on 3 impulse waves up in the main direction.

And 2 corrections against the main trend.

A total of 5.

An over- simplification. But, again, you get the idea.

Like last week’s article on Elliott Wave, where do I stop.

I could go on. Maybe I've piqued your interest.

I’ve tried to make this interesting. Giving you some tidbits to walk away with.

If I’ve lost you, I’m sorry.

Fibonacci and Elliott Wave go hand in hand.

It is a science that does exist.

It is an art form, and a skill, deciphering it in real time.

One is attempting to make a forecast from analysis.

Trying to know where the market is. Trying to know where your investments are. At the present moment.

For example, in 1720, at the top of the South Seas Bubble,

you did not want to be long the market. There were 64 years to go before a bull market started up again. (Interestingly, this coincided with the American and French Revolutions.)

In 1830, you didn't want to be long the market. It was 30 years before ‘back-to-par’ happened.

Same in 1929. It took 30 years for the Dow Jones to get back to 400.

I don't know about you, but, I don't wanna have to wait 30 years for my money to come back from a “big” correction. Or a depression.

Minor “dips” - weekly ones, monthly ones, we can weather these.

(This is what I alluded to in an earlier LinkedIn article, 10.4.19 – “Context”.)

But, in any downtrend of larger size, preservation of capital is of paramount importance. (Also, an earlier article – “Preservation of Capital”, LinkedIn, 10.7.19)

Maybe you're interested and fascinated by Elliott Wave and Fibonacci but don't have the time to study it. My suggestion to you - get a subscription to Elliott Wave International.

Their Elliott Wave Financial Forecast is their everyday “bread-and-butter” analysis. Steve Hochberg and Pete Kendall edit this monthly.

A 3X-a-week Short Term Update is also put out every Monday, Wednesday and Friday.

They do the work for you and you reap the benefits.

Robert Prechter edits The Elliott Wave Theorist. This is a more macro, more overview, and more theoretical publication. It's more like an article or a white paper. It’s put out monthly. Unless a “Special Interim Bulletin” is thought to be necessary.

If you want to delve into any underlying themes or theories of Elliott Wave and more,

read Robert Prechter's Socionomic Theory of Finance.

(It's a big book, but, it's interesting. Then again, probably only if you're a mathematics geek.)

(I am not compensated for this endorsement.

I have been an on-again, off-again subscriber since 1991.

I believe. IA)

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