0, 1,1, 2, 3 … Happy Fibonacci Day!

0, 1,1, 2, 3 … Happy Fibonacci Day!

You may have never heard of the Fibonacci sequence, but it’s a mathematical formula that has been around for hundreds of years and is used to analyse financial markets. This article will explore the Fibonacci sequence and why it’s so important.

What is the Fibonacci Sequence?

The Fibonacci Sequence is a series of numbers that starts with 0 and 1, and each subsequent number is the sum of the previous two. So, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… and so on indefinitely.

Where did it come from?

In 1202, an Italian mathematician named Leonardo Fibonacci published a book called Liber Abaci (Book of Calculation). In it, he introduced the Hindu-Arabic numeral system to the Western World. He also popularised a simple numerical sequence in which each number is the sum of the previous two (the Fibonacci sequence).

Why is it so important?

Well, the Fibonacci Sequence appears in nature quite often! 
It can be found in the arrangement of leaves on a stem, the pattern of petals on a flower (typically come in sets of 3s or 5s), or even in spiral galaxies. Also, many animals have body parts that follow the sequence – for example, a rabbit has five toes on its front paws and three on its back paws. 
It also has applications in mathematics, art, architecture and financial markets. For example, the golden ratio – is characterised by the fact that the quotient between any term in the series and the preceding term always tends to the same value (1.618) as you progress through the series. This proportion occurs often in nature and has been used by artists such as Leonardo da Vinci to create aesthetically pleasing compositions, like Mona Lisa and Vitruvian Man.
Golden ratio calculation/demonstration:
1/1 = 1
Vitruvian Man by Leonardo da Vinci
Vitruvian Man by Leonardo da Vinci

What are the Benefits of Learning About the Fibonacci Sequence?

If you enjoy maths, then learning about the Fibonacci sequence can be a fun and interesting way to explore a fascinating mathematical concept. Even if you don’t particularly enjoy maths, understanding the Fibonacci sequence can still offer some benefits. Here are a few reasons why learning about the Fibonacci sequence can be beneficial:
1. Help improve your problem-solving skills.
The Fibonacci sequence is all about patterns and relationships between numbers. Understanding it can help you become better at spotting patterns and solving problems in general.
2. Make you appreciate maths more.
Let’s face it: for many people, maths is not an enjoyable subject. However, the Fibonacci sequence is a perfect example of how maths can be beautiful and fascinating. Learning about it may just make you appreciate maths a little bit more.
3. Help you understand nature better.
The Fibonacci sequence is found throughout nature, from the arrangement of leaves on a plant to the spiral of a seashell. Understanding this connection between mathematics and nature can help you appreciate both subjects more.
Fibonacci sequence number in spiral
Fibonacci sequence number in spiral

Fibonacci sequence in financial markets

In economics, several concepts are based on Fibonacci numbers, including Fibonacci retracements/expansion and Elliott Wave Principle.
These concepts help technical analysts to define more precisely the key points of trend changes and movement corrections, for example: if the market is moving up and then suddenly reverses direction, it might be because it has reached a Fibonacci expansion or retracement level. This level could be a support or resistance level that traders watch for clues about where the market is headed next.
Fibonacci levels are especially important to day traders who look for short-term opportunities in the market. By understanding how Fibonacci levels work, day traders can better predict when to enter and exit trades.


1. The use of the golden ratio is the secret of the world’s most resistant structures such as the Great Pyramid of Quéops ( Khufu ) built around 2560 B.C;
2. The seeds of a sunflower are usually arranged in two groups of spirals in the core of the flower: 21 clockwise and 34 counterclockwise;
3. If a person of average stature divides his height by the distance between his navel and his head, the result will be around 1.618;
4. As already mentioned, the Fibonacci sequence is found in Leonardo da Vinci’s “Mona Lisa” in the relationship between the torso and the head of the depicted figure as well as in the elements of the face;
5. Each block of the Egyptian pyramids is 1,618 times smaller than the one below it.


The Fibonacci sequence is a mathematical concept that has many applications in the real world. It can be used to predict population growth, calculate financial risks, and even understand animal proportions. While it may seem like a dry topic, understanding Fibonacci can provide insights into some of the most fascinating patterns in nature. So on this Fibonacci Day, take some time to learn about this incredible sequence and its far-reaching implications.
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Amândio Luís

Amândio Luís

Technical Analysis Explained

Technical analysis is the study of past market data in order to help predict future prices. It does this by examining trading volumes and trends, price changes and other events associated with the market. In this blog post, you’ll learn more about technical analysis – including its definition, some of the concepts and who uses it.

What is Technical Analysis?

Technical analysis is the process of using past price data to identify market trends and make future price predictions. The experts in the field believe that prices move in cycles and that these cycles can be identified and used to make trading decisions.
Many different techniques can be used, but some of the most popular include trend line analysis, support and resistance levels, and candlestick charting. Technical analysts will often use a combination of these techniques to make the most accurate predictions possible.
While technical analysis can be used in any time frame, it is most commonly used by day traders or short-term traders who are looking to take advantage of small price movements.
Candlestick chart used in technical analysis
Candlestick chart


Technical analysis is a security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume.
The benefits of technical analysis are numerous, but some of the most notable include:
1. The ability to identify trends: One of the primary goals of technical analysis is to identify whether a security is in an uptrend, downtrend, or sideways trend. This information can be used to make informed decisions about when to buy or sell a security.
2. The ability to forecast future prices: Technical analysts use historical price data and other market indicators to try and predict where prices are headed in the future. While no one can predict the future with 100% accuracy, technical analysis can give investors an edge in making investment decisions.
3. The ability to make better-informed decisions: By taking into account factors such as trends, support and resistance levels, and price patterns, technical analysis can help investors make more informed decisions about when to buy or sell a security. This can lead to improved investment returns over time.


There are a few disadvantages to be aware of. First, past performance is no guarantee of future results – what worked in the past may not work in the future. Second, technical analysis is based on price and volume data, which can be subject to interpretation. And third, even with the best tools and indicators, success in trading still comes down to human factors like psychology and emotion.

Who uses technical analysis?

Technical analysis is used by a wide variety of market participants for different purposes. Some use it to attempt to identify patterns that may indicate a future market direction, while others use it to generate trading signals or develop trading systems. There are also those who use technical analysis as part of a more comprehensive investment strategy that includes other factors such as fundamental analysis and risk management.
The common thread among all users of technical analysis is the belief that past price data can provide insights into future market behaviour. As a result, technical analysts believe that it is possible to identify patterns in past price data that can be used to predict future market movements.
One of the most important things to remember about technical analysis is that there is no one right way to do it. Different analysts may use different methods and indicators, and there is no guarantee that any particular approach will be successful. Technical analysis is an art as much as it is a science, and each analyst brings his or her unique perspective to the table.
Person doing technical analysis in a computor
Technical Analysis


Technical analysis is a powerful tool that can help traders and investors identify opportunities in the market. However, it is important to remember that technical analysis is not an exact science, and there is no guarantee that every signal will result in a profitable trade. Nevertheless, by understanding and correctly applying the concepts of technical analysis, traders and investors can give themselves a better chance of success in the financial markets.
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Author: Amândio Luís

Author: Amândio Luís

Technical Analysis Explained