What Is the Fibonacci Sequence?

When we speak of mathematics, beautiful is a word seldom used. However, on the rare instance that it is, mathematics manages to capture the essence of the word quite aptly that one has to stop and wonder why it isn’t used more often.

One such instance of beauty is the discussion of the concept of the Fibonacci Sequence. If we start at the smallest possible positive integer, that is 1, and follow a continuous, non-exhaustive pattern wherein we add the last two numbers, we would reach what is commonly referred to as the Fibonacci sequence and sometimes admiringly referred to as “nature’s secret code.”

Practically, if we start at 1, the number before 1 would be 0. Thus, using 0 and 1 as our base for the sequence, if we begin to add the last two numbers and add the answer to the pattern, we would arrive at 0, 1, 1. This is because 0+1=1.

If we continue the pattern and satisfy the condition of adding the last two numbers, the answer according to the new sequence would be 2, because 1+1=2, rendering our pattern to now be 0, 1, 1, 2. If we continue, the pattern will begin to look like 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. 

This pattern was popularized by Leonardo Pisano, who is also known as Fibonacci. Named after him, each integer in this pattern is called a Fibonacci number, and the pattern itself is called the Fibonacci Sequence.

What Is Fibonacci Retracement?

Fibonacci ratios are a series of important key numbers produced by analyzing any two extreme points within the sequence. These “key numbers'' are ratios called the Fibonacci retracement levels. They were devised by Leonardo Fibonacci in the year 1,170 AD. Some of these, as illustrated in the graph above, include: 23.6%, 38.2%, 50%, 61.8%, and 78.6%.

When Fibonacci retracement levels are used in finance, they are shown by horizontal lines which signify resistance and support levels for a particular asset. Each ratio or %age corresponds to one of the Fibonacci retracement levels. It shows exactly how much the price has pushed to reverse a prior trend. The previous trend is projected to continue in the same manner, however, the price of the asset usually retraces back to one of the above-mentioned Fibonacci ratios before that happens.

Every single number in the Fibonacci sequence is the cumulative sum of the two numbers before it, and each Fibonacci number (except the first few numbers) is approximately 1.618 times larger than the one before it. For example, 55 and 89 are two subsequent Fibonacci numbers. 55 multiplied by 1.618 gives us 88.99, which is almost 89. Furthermore, 1.618 is what some mathematicians refer to as the Golden Ratio.

The Fibonacci levels, on the other hand, can be found easily by simply dividing the Fibonacci numbers. The ratio or level of 61.8%, for example, can be determined by dividing 21 by 34, or 55 by 89. The same practice of division is true for almost every other Fibonacci number except the first few.

How to Use Fibonacci Retracement

When these levels are used in finance to predict support and resistance levels, they are called Fibonacci retracement. In the capital sector, Fibonacci ratios are used to determine the price momentum of any given asset. They are used by analytical traders to construct support lines and illustrate resistance levels so that they can protect their monetary investment by setting stop-losses at crucial Fibonacci levels and establishing take-profit goals.

If you wish to use Fibonacci retracement, there are tools that can help, but here is a general guide on using it:

1. First, identify the market trend. Is it an upward trend or a downward one?

2. Depending on the trend, use the Fibonacci retracement tool. In an uptrend, attach it to the bottom and take it to the top by dragging it to the right. Do the opposite in a downtrend by attaching it to the top and taking it to the bottom by dragging it to the right.

3. In an uptrend, you can monitor the possible support levels. In a downtrend, you can monitor the possible resistance levels. The Fibonacci retracement tool will point out these levels to you.

As important as a Fibonacci retracement is, do not entirely rely on it. The results and predictions are shockingly similar to market trends, but they are not absolute or set in stone. The market will not automatically reverse the trend just because the price point reached a Fibonacci level.

Why Is the Fibonacci Sequence So Important?

Almost every time a mathematical conundrum is presented, we curious beings wonder about its plausible applications. What makes any conundrum important? Perhaps the significant number of uses they offer, or perhaps the explanations of things otherwise inexplicable?

So, what makes the Fibonacci sequence so important, and why is it deemed “nature’s secret code” by some? Due to the previously mentioned Golden Ratio of 1.618, the Fibonacci sequence is remarkable and indispensable. Many things in nature, from the number of veins on the leaf of a plant to the angle at which leaves grow on stems, can be explained by the golden ratio.

The Fibonacci sequence is so important because it helps us understand how many scientific wonders are not mere wonders but rather calculated decisions that nature makes, including spiral galaxies and hurricanes.

Furthermore, the applications of the Fibonacci sequence are vital to many computer algorithms. Surprisingly (or maybe not-so-surprisingly), even music can make use of the golden ratio!

What Is Fibonacci Spiral and How to Draw It?

The Fibonacci sequence gives us the Fibonacci spiral, which is a spiral that grows larger outwards (just like the numbers in the sequence). The Fibonacci spiral is oftentimes used in architecture and interior designing.

If you’re interested in knowing how to draw it, it’s pretty simple. You will need a pencil, a ruler, and some grid paper. The bigger your grid paper is, the bigger your spiral will be.

1. You will start by making squares that follow the Fibonacci numbers. Make a square somewhere around the center of the page, with each side equal to a Fibonacci number. You can start by making a 1x1 square, meaning it will be just one box on your grid paper.

2. Then, following the pattern 1, 1, 2, 3, 5, 8, and so on, make squares counter-clockwise with each subsequent square being the next Fibonacci number in line. Refer to the drawing of the squares above to understand the placement.

3. After your squares are made, use your hand’s natural movement or use a compass for smoother lines and follow the spiral drawing as shown above.

4. As an optional measure, if you would like only the spiral and no squares, you can draw your spiral with ink and later erase the squares behind.

Many designers worldwide make use of the Fibonacci spiral. Thanks to the Fibonacci sequence, mathematicians and artists alike can make use of the same concept. That goes to show how integral this concept is.