Over the years, the Fibonacci sequence has become a topic of interest that has gotten the attention of many people. This could be due to its mathematical properties or close connection to the golden ratio, a proportion (roughly 1:1.6) that often occurs throughout the natural world and is applied in many human endeavours.
The Fibonacci sequence put is the sum of two numbers preceding it in the sequence. This sequence is of interest to physicists and biologists as it is always observed in different phenomena and natural objects. The Fibonacci sequence and the golden ratio are employed to help guide architecture designs, user interfaces, websites, and so on.
Are you seeking to know more about the Fibonacci sequence? Then take your time to go through this article as it reviews important pieces of information about Fibonacci’s sequence to help you have a good understanding of it.
What is the Fibonacci sequence?
The Fibonacci sequence is a set of numbers that begins with a zero or one, followed by a one. It increases further based on the rule that each number (Fibonacci number) equals the sum of the two preceding numbers.
The expression of the Fibonacci sequence, when written, as a rule, is as follow;
Xn = Xn-1 + Xn-2
Fibonacci numbers are created by ratios found in Fibonacci’s sequence. In some cases, the first two numbers are defined as 0 and 1, for instance;
F(0) = 0,1,1,2,3,5,8,13,21,34…….
While others are defined as 1 and 1 by default as shown below;
F(1) = 1,1,2,3,5,8,13,21,34…….
This sequence is named after an Italian mathematician known as Leonardo Pisano or Fibonacci. He was able to use the arithmetic sequence to solve a problem based on a pair of breeding rabbits.
Although many people might look at this sequence as a simple brain teaser, it can be proven to be very useful in solving problems, especially in the following fields of study; statistics, computer science, nature, agile development, and advanced development mathematics.
Reasons why using the Fibonacci sequence makes you better at estimating.
1. The Fibonacci sequence reflects uncertainty.
The Fibonacci sequence assigns smaller values to the user story, which helps show that the story is well understood. In contrast, the user story follows INVEST (independent, negotiable, valuable, estimable, small, and testable) guidelines.
Moreover, large values assigned by the Fibonacci sequence helps to denote that the story is not well understood or needs to be well explained. Teams can easily and confidently estimate smaller stories in detail.
It is a usual practice by the matured Agile teams to restrict the Fibonacci sequence up to 21 (0,1,1,2,3,5,8,13,21). Stories of this size are easy to understand, while stories beyond 21 needs to be further broken down. This practice helps to prevent greater uncertainty and also helps the team to write better stories while making use of the INVEST guidelines.
2. The Fibonacci sequence helps in comparison.
The Fibonacci sequence helps individuals be better at comparison than estimation since it can be easily understood and adopted by the team. The Fibonacci sequence has different values and easy sequence, which helps to estimate by comparison rather than by measuring the object.
3. Application of Weber-Fechner law
The laws are related to human perception and closely related to actual changes in physical stimuli and perceived changes. The stimuli include the 5 human senses: hearing, vision, taste, smell, and touch.
This law can be applied to numerical cognition. For instance, psychological research shows that it becomes more difficult to discriminate between two numbers, especially when their difference decreases. This concept is known as the distance effect, and it is valuable in areas of magnitude estimation that deal with large scales and estimating distances.
The Fibonacci sequence is very much similar to weber’s law. For instance, the approximate diameter of a cricket ball is around 2.8 to 2.86 inches, while that of a football is around 8.66 inches. With this example, it is very easy to distinguish between the relative sizes of the two since the diameter of a football is approximately 3 times that of a cricket ball.
Although it would be difficult to distinguish between two cricket balls that have 1 inches diameter difference, while you try to measure both. In this type of scenario, the Fibonacci sequence can help to distinguish the sizes. This is because the relative size between two adjacent numbers in the Fibonacci sequence is 60%, enabling it to size both balls accordingly.
4. The Fibonacci sequence is composed of integers.
It is most suitable to use integer’s scales when estimating the time it would take to complete a task. Since the aim of estimating tasks in Agile is a high-level estimate, integers or whole numbers are needed to estimate as there is no use for granularity of 2.4 and 3.2.
5. The Fibonacci sequence is exponential.
A Fibonacci sequence is an exponential tool that helps provide details for small tasks and forces uncertainty for large tasks. This feature makes it very suitable for estimating time.
6. The Fibonacci sequence is non-linear
This feature of the Fibonacci sequence helps to reduce over-analysis. For instance, out of 6 numbers used, 4 would be prime numbers; this reduces your ability to compare or break down tasks evenly.
Some pros and cons of using Fibonacci at trading
- It is very versatile. The Fibonacci sequence can be used on any timeframe and also used on assets of any market. However, the accuracy of the signal depends on the timeframe; as the higher the timeframe, the more accurate the signal is.
- The Fibonacci sequence serves as a tool to determine the accuracy of pivot points. When it is correctly set, Fibonacci can accurately help determine the stages of price reversals early or help to confirm changes in the direction of the trend at later levels.
- With the Fibonacci sequence, you can have accurately displayed market psychology. This is because most market technical indicators are based on the formula, which shows patterns of former periods.
- The Fibonacci is not suitable for algorithmic strategies; hence cannot be used in expert advisors. This is because it is not possible to write an automatic grid building algorithm into the EA code.
- It can provide false signals. This is a usual occurrence when making use of this tool. This might result from a turnaround of price without reaching the predicted level or after breaking it.
- There is the difficulty of determining the starting point when using Fibonacci since trends are never perfectly flat.
With the many benefits attached to the Fibonacci sequence, we can ascertain that this sequence is very valuable in solving related mathematical problems and used by biologists and physicists in different phenomena and natural objects. It can also be used in trading as it is versatile, accurately determine pivot points and market psychology.