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What are Fibonacci Numbers?

Exploring Fibonacci Numbers: Their History and Value in Research

Fibonacci numbers are an integral part of the Fibonacci sequence, a series of numbers in which each number is the sum of the two preceding numbers. This sequence begins with 0 and 1, so the third number is 0+1=1, the fourth number is 1+1=2, the fifth number is 1+2=3, and so on. This sequence continues infinitely, resulting in a fascinating pattern of numbers.

The Golden Ratio and Fibonacci Numbers

One of the most intriguing aspects of Fibonacci numbers is their connection to the Golden Ratio. The Golden Ratio is a mathematical constant approximately equal to 1.61803398875, often denoted as Phi (Φ). This ratio is derived from the relationship between consecutive Fibonacci numbers as they progress in the sequence.

The Golden Ratio has captivated mathematicians, artists, and architects for centuries due to its aesthetically pleasing proportions. It has been used in various forms of design, including architecture, art, and even music. The Golden Ratio is believed to represent perfect harmony and balance, and its influence can be observed in nature, as well as human creations.

Fibonacci Numbers in Nature and Fractals

The presence of Fibonacci numbers extends far beyond mathematical sequences. These numbers are found in nature, particularly in the realm of fractals. Fractals are intricate, self-similar patterns that repeat at different scales. They can be observed in natural phenomena such as the branching of trees, the spirals of seashells, and the arrangement of flower petals.

Fibonacci numbers appear in various aspects of these fractal patterns, contributing to their intricate beauty and complexity. The relationship between Fibonacci numbers and fractals highlights the underlying mathematical order that exists in seemingly chaotic natural systems.

Fibonacci Numbers in Trading and Research

Fibonacci numbers and their associated ratios have also found applications in the field of trading and market analysis. Many traders utilize a tool called Fibonacci retracements to predict and interpret market swings. Retracements occur when a strong trend temporarily reverses before continuing in its original direction.

The theory behind Fibonacci retracements is based on the idea that complex systems, such as financial markets, exhibit some degree of orderliness. Traders use Fibonacci levels as potential support and resistance areas, where prices are likely to pause or reverse. The Fibonacci retracement levels, derived from the Golden Ratio, serve as reference points to identify potential entry or exit levels in the market.

While the use of Fibonacci numbers in trading is still evolving, advancements in computing power have allowed traders to uncover patterns and relationships within market data. The integration of artificial intelligence services, such as those offered by Tickeron, further enhances traders' ability to analyze signals, evaluate trade ideas, and make informed trading decisions.

The Controversy Surrounding Fibonacci Studies

Like any trading tool or strategy, Fibonacci studies have both proponents and skeptics. Some traders firmly believe in the predictive power of Fibonacci numbers and rely on them to make significant trading decisions. They view these tools as valuable additions to their technical analysis toolkit.

On the other hand, there are those who view Fibonacci studies with skepticism, considering them to be exotic mathematical curiosities that may have limited influence on market dynamics. They argue that the popularity of Fibonacci tools among traders may even create self-fulfilling prophecies, potentially impacting market behavior.

Fibonacci numbers, with their fascinating mathematical properties and their connection to the Golden Ratio, have intrigued scholars, artists, and traders alike for centuries. From their influence on architecture and design to their application in market analysis, Fibonacci numbers continue to captivate and inspire.

While the efficacy of Fibonacci studies in trading is a subject of debate, they remain a valuable research tool for many investors. The interplay between mathematics and financial markets offers intriguing insights and potential patterns that can aid in decision-making processes. Whether one fully embraces Fibonacci studies or approaches them with caution, exploring their potential within the realm of trading can be an enlightening and thought-provoking journey.


Fibonacci numbers are part of the Fibonacci sequence, where the two previous numbers are added together to calculate the next number in the sequence. The ratio of two Fibonacci numbers is the Golden Ratio, or 1.61803398875, which has been used since ancient times as the perfect proportion in architecture and other design. The Golden Ratio is also known as Phi (pronounced “fee”). Because Fibonacci numbers are found throughout the natural world, they have been integrated into some traders’ strategies for market analysis.

Modern computing power has uncovered plentiful examples of the Golden Ratio in nature, from Nautilus shells to musical harmonics, as well as in mathematical fractal patterns. Fibonaccii numbers are related to the study of chaos theory, which seeks to find order in complex systems. Since the markets have so many variables, but no lack of data, they are an excellent place to search for Fibonacci patterns.

Many traders use Fibonacci Retracements to predict or interpret the swings of the market, and many compelling examples exist of Fibonacci retracements seeming to indicate where trends would start and stop.

Retracements are defined as points where a strong trend “retraces its steps” and is momentarily set back by a smaller reverse trend before continuing the previous stronger trend. The theory behind Fibonacci Retracements is that complex systems will exhibit orderly behavior to some extent. The so-called random walk of stock prices has been shown to fit on occasion into the parameters of Fibonacci lines and arcs.

The use of Fibonacci numbers in trading is still in its early stages, but ever-growing computing power available to traders increases their ability to find the common threads that will make this investment theory more usable, accurate, and reliable. These include artificial intelligence services from Tickeron, which provide traders with powerful ways to evaluate trade ideas, analyze signals, and provide key confirmation to help investors make rational, emotionless, and effective trading decisions.

Tickeron's Offerings

The fundamental premise of technical analysis lies in identifying recurring price patterns and trends, which can then be used to forecast the course of upcoming market trends. Our journey commenced with the development of AI-based Engines, such as the Pattern Search Engine, Real-Time Patterns, and the Trend Prediction Engine, which empower us to conduct a comprehensive analysis of market trends. We have delved into nearly all established methodologies, including price patterns, trend indicators, oscillators, and many more, by leveraging neural networks and deep historical backtests. As a consequence, we've been able to accumulate a suite of trading algorithms that collaboratively allow our AI Robots to effectively pinpoint pivotal moments of shifts in market trends.

Disclaimers and Limitations

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