# Leonardo Fibonacci - Background

Leonardo Fibonacci (1170 – 1280), pronounced "Fi-bon-a-chi", gets credit for what is known as the Fibonacci number sequence. But let me first give you a little of the back story. As with most of history, it is usually presented in a biased fashion through the eyes of the author.

While Leonardo Fibonacci may get all the credit for the number sequence, it was actually discovered by ancient Hindu mathematicians.

As the story goes, any last transcripts from the Hindu mathematicians number sequence were lost. It was only through Leonardo's efforts to document the number sequence and its relationships that actually saved the ancient Hindu mathematician's work. Without Leonardo taking the time to document the mathematicians work, the "Fibonacci" numbers and the number sequence would have been lost forever.

In the end, Leonardo's documentation has proven to be some of the last transcripts regarding the topic and the Hindu mathematicians work. And thank goodness he did save the mathematicians work - it has proved to be an invaluable tool in my charting toolbox.

# Calculate The Fibonacci Number Sequence

So what are the Fibonacci numbers? First I think it is important to start with the methodology used to calculate the Fibonacci number sequence. The numbers in the Fibonacci number sequence are calculated in a very methodical fashion. Let me walk you through the steps to develop the sequence yourself.

Write down the numbers 0 and 1. These are the very first two whole numbers and also make up the first two numbers in the Fibonacci number sequence. After writing them down, add the numbers together.

Write down the answer to the formula, 1, after the first two numbers in the sequence you wrote down. The sequence now has three numbers in it and should look like this 0 1 1. Let's calculate the next number in the sequence, the fourth number overall.

The fourth number in the sequence is calculated by adding together the last two numbers in the developing sequence. The last two numbers in the sequence of 0 1 1 sequence are 1 & 1. Add those numbers together.

Write down the answer of 2 at the end of your developing Fibonacci number sequence. The developing number sequence should now look like this 0 1 1 2.

To calculate the fifth number in the sequence, repeat the same steps for the fourth number - select the last two numbers from the end of the Fibonacci number sequence 0 1 1 2. The last two numbers are 1 & 2. Add those numbers together.

Place the result of 3 at the end of the current number sequence. The Fibonacci number sequence that we have calculated so far is 0 1 1 2 3.

To calculate the next number in the sequence, add the last two numbers from the end of the developing Fibonacci number sequence 0 1 1 2 3. The last two numbers are 2 & 3. Add those numbers together.

Place the result of 5 at the end of the current number sequence. The Fibonacci number sequence that we have calculated so far is 0 1 1 2 3 5.

To calculate the next number in the sequence, add the last two numbers from the end of the developing Fibonacci number sequence 0 1 1 2 3 5. The last two numbers are 3 & 5. Add those numbers together.

This process and the Fibonacci number sequence can be carried out to infinity. I did a handful of additional calculations and carried out the number sequence to 2,178,309.

# Fibonacci Numbers & Fractals In Everyday Life

Fibonacci numbers are present in almost every aspect of every day life and their surroundings, yet most people are not aware of this phenomenon. For example, each picture in the following mosaic represents a Fibonacci number or has a Fibonacci relationship of some sort.

# The Golden Spiral & Golden Ratio

A golden spiral occurring in nature can be seen in the development of a sea shell, like the one featured above.

The arc of a golden spiral expands at a factor of 1.61803398875 as illustrated. This factor is typically referred to as the golden ratio. In summary, there is a golden spiral and a golden ratio.

The golden spiral is reflected in a charting tool - the Fibonacci spiral tool.

The golden ratio is typically expressed as a percentage - 161.8%. This percentage is key ratio for sustaining "growth" throughout the universe. Growth can be measured in terms of living biological creatures or even stock prices.

As a Trendy Stock Charts member, you will see how I use the golden ratio to my favor when I calculate buy and sell targets for stocks. The precision of the calculated buy and sell targets using a golden ratio is second to none.

## The Fibonacci Relationship of phi

There is an interesting relationship as the above fibonacci number sequence develops. If you take any number in the sequence and divide it by the number immediately following it, the resulting ratio always approximates .618 or 61.8% or phi. Let me show you a few examples.

Start by selecting any set of sequential numbers from the above fibonacci number sequence. I randomly selected 89 and 144 as the sequential numbers for this calculation.

### 89 ÷ 144 = .618 (phi)

Let's take another set of sequential numbers from the fibonacci number sequence, the numbers 5 and 8. These numbers are actually the lowest set of numbers in the Fibonacci number sequence that will produce phi (it is actually off just a little - .007).

### 5 ÷ 8 = .625 (almost phi)

And let's perform one last calculation to ensure you are familiar with the calculation of phi. This time I will use a larger set of numbers in the sequence, 1,597 and 2,574.

### 1,597 ÷ 2,574 = .618 (phi)

It does not matter where the sequential numbers are at in the Fibonacci number sequence, the end result will always be phi.

# Phi or phi? Don't Get Confused!

It is extremely important that you do not confuse phi with Phi, even though they are closely related to each other.

If you do happen to mix up phi and Phi, it can cause you to calculate a target price that may never get achieved! There is nothing worse than waiting for a price target that never arrives. Instead, you sit there watching... patiently waiting...and waiting...and waiting...and losing profits...and waiting...and waiting...

In order to avoid any confusion in my stock articles, I will refer to phi as phi; I will refer to Phi as the golden ratio. A lot of times, I refer to the golden ratio and phi by their percentages of 161.8% and 61.8% respectively.

If you ever notice phi at the beginning of a sentence and it is not capitalized? It could mean that I am referring to phi and not Phi. Very confusing. Just remember, phi does not mean the same as Phi. Join Trendy Stock Charts and I will help to wipe away any confusion between the two and show you how they can both lead to more accurate price projections.

# Fibonacci Analysis & Charting Tools

How does phi and the Golden Ratio relate to the stock market? Well these ratios are represented in the various Fibonacci Charting Tools, such as the Fibonacci Extension Tool, Fan Tool and Retracement Tool.

Fibonacci charting tools can be used to calculate price targets in any market conditions. The results from using Fibonacci charting tools can provide specific price targets to buy or sell stocks. It is imperative to know the different uses for each Fibonacci tool. If you are only using each tool for one thing, you are not using all of its potential.

In the Trendy Stock Charts members area, I discuss the proper placement of the Fibonacci tools on stock charts. I've discovered that it helps to have a working knowledge of Elliott's Wave Theory for Fibonacci tools. Elliott wave theory is one of my favorite technical analysis methods.

Achieving consistent success using Fibonacci analysis & tools takes a lot of practice. Learning the proper placement areas for the tool's anchor points is essential. I discuss various hazards and pitfalls to be aware of when using these tools. This is not rocket science. Technical analysis can be learned. Especially when you have someone willing to guide you like I am.

# Join Trendy Stock Charts

If you have ever wanted to learn Fibonacci analysis, you have come to the right place. As a Trendy Stock Charts member, you have access to all my premium stock articles where I break down stock charts using phi and the golden ratio. There are not many articles where I am not discussing either phi or the golden ratio on a stock chart. They are that important.

Trendy Stock Chart members have access to detailed, step-by-step information on placing Fibonacci tools on charts. I review the best practices for each tool and also the pitfalls to avoid with them. The golden ratio and phi can be seen as lines of measurement all the Fibonacci charting tools.

After becoming a Trendy Stock Charts member, stop by the Idea Chamber and ask me to break down your favorite stock chart using Fibonacci analysis. The precision of the results from using Fibonacci charting tools will leave you breathless. As usual, I will come up with specific buy, sell or hold recommendations based on the results of the Fibonacci analysis.