What is the Fibonacci sequence?

The Fibonacci sequence is an infinite succession of natural numbers, first described by the Italian mathematician Fibonacci in the 13th century. This number series begins with 0 and 1, continuing with the sum of the two previous numbers to infinity: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.

The Fibonacci sequence is part of many systems, even in nature, for example, it is found in the arrangement of tree branches, flower petals and leaves on a stem, the sunflower being the most precise example. Each of the Fibonacci numbers approximates the so-called golden ratio, or number of gold, representing natural geometric perfection.

This series of numbers consists of a ratio that has been used for centuries in numerous areas, from architecture, art, and today even in stock market analysis and programming areas.

History.

Around the year 1202, Leonardo de Pisa (Fibonacci) was a young Italian who, on his travels to the East, discovered the existence of Arabic numerals. Upon his return, he wrote the book "Liber Abaci", in which he transferred the mathematical knowledge of the Orientals to Europe.

Fibonacci promoted the new number system, considering it easier on business skills than the Roman numerals used in his day. The concern that led him to postulate the famous sequence that bears his name was to learn about the mating habits of rabbits. Fibonacci concluded that:

• During the first month, there are a few rabbits and, as they are not old enough, they cannot reproduce.
• During the third month, the first pair breeds for the first time, so there are 2 pairs of rabbits.
• In the fourth month, the first pair breeds again, so there are three pairs.
• During the fifth month, the first pair reproduces and the second pair reproduces, although the third pair is still very young, so there are five pairs.
• This sequence continues.

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Applying the Fibonacci sequence in project management

The mathematical rule of the Fibonacci sequence has several applications today, and is very useful for working on projects with Scrum methodology.

In this case, it is used to evaluate task effort with so-called story points. They are part of an estimation technique called Planning Poker, using the cards from the popular game.

In Scrum, estimates are made in the sprint in which it is evaluated what work can be executed successfully with the team. When working with these points, it is about a personal and particular assessment of the team that will tackle the task and its difficulty. In these cases, the Fibonacci sequence is used to award points and, in this way, estimate the complexity to be able to work with sprints of between 1 and 4 weeks, since these are cyclical: when one ends, another begins.

When holding a sprint planning meeting, the point estimation process consists of several stages. In the first, the person who holds the position of Product Owner (PO) and the Scrum Master together with the team seek to estimate the user stories. Then, each member of the team estimates a number from the Fibonacci sequence that they think can represent the complexity of the task and the effort that can be endured. Subsequently, all team members show the number they have chosen. The team will agree to choose a number: in this way, everyone will be involved and will be responsible for the success or failure of the sprint since the estimate is based on consensus.

In these cases, the distance between the numbers reflects that the uncertainty of the estimate grows proportionally with the size of the element. In addition, zero is maintained for elements that do not require effort.

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Conclusion.

The Fibonacci sequence, even centuries after its formulation, has practical implications in daily life and particularly within project management. Historically, this succession of numbers has helped to make estimates.

The reason for the success of the Fibonacci sequence is that after the first two numbers, each number is approximately 60% larger than the previous value. So the Fibonacci values work fine as they increase by roughly the same ratio each time.