Summary: The Fibonacci Sequence is a peculiar series of numbers from classical mathematics that has found applications in advanced mathematics, nature, statistics, computer science, and Agile Development. Let’s delve into the origins of the sequence and how it applies to Agile Development.

## What Is The Fibonacci Sequence?

The Fibonacci sequence is a series of numbers where a number is the addition of the last two numbers, starting with 0, and 1.

**The Fibonacci Sequence:****0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…**

Written as a rule, the expression is:

**X _{n} = X_{n-1} + X_{n-2}**

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### The Fibonacci Spiral And The Golden Ratio

The Fibonacci sequence is often visualized in a graph such as the one in the header of this article. Each of the squares illustrates the area of the next number in the sequence. The Fibonacci spiral is then drawn inside the squares by connecting the corners of the boxes.

The squares fit together perfectly because the ratio between the numbers in the Fibonacci sequence is very close to the golden ratio [1], which is approximately 1.618034. The larger the numbers in the Fibonacci sequence, the closer the ratio is to the golden ratio.

The spiral and resulting rectangle are also known as the Golden Rectangle [2].

### The Origins Of The Fibonacci Sequence

Fibbonaci (Leanardo Pisano Bogollo [3], Fibonacci was his nickname) first introduced the series of numbers known as the Fibonacci sequence in his book *Liver Abaci* [4] in 1202. Fibonacci was a member of an important Italian trading family in the 12th and 13th century. Being part of a trading family, mathematics was an integral part of the business. Fibonacci traveled throughout the Middle East and India and was captivated by the mathematical ideas from his travels. His book, *Liver Abaci*, was a discourse on the mathematical methods in commerce that Fibonacci observed during his travels.

Fibonacci is remembered for two important contributions to Western mathematics:

- He helped spread the use of Hindu systems of writing numbers in Europe (0,1,2,3,4,5 in place of Roman numerals).
- The seemingly insignificant series of numbers later named the Fibonacci Sequence after him.

Fibonacci discovered the sequence by posing the following question:

If a pair of rabbits is placed in an enclosed area, how many rabbits will be born there if we assume that every month a pair of rabbits produces anotherpairand that rabbits begin to bear young two months after their birth?

- Start: At the start no rabbits are born, as the initial pair has not had time to be pregnant and born
**(0)**. - The first month: One pair of rabbits are born
**(1)**. - The second month: Again, one pair of rabbits are born as the new rabbits have not yet matured to bear young
**(1)**. - The third month: Two pairs of rabbits reproduce, and one pair is not ready, so two pairs of rabbits are born
**(2)**. - The fourth month: Three pairs of rabbits reproduce and 2 pairs of rabbits are not ready, so three pairs of rabbits are born
**(3)**. - The fifth month: Five pairs of rabbits produce and three are not ready, so five pairs of rabbits are born
**(5)**. - And so on.

Though Fibonacci’s question concerning the rabbits is an unrealistic scenario, the sequence can be observed in nature, such as in the array of sunflower seeds and other plants, and the shape of galaxies and hurricanes.

Sunflower Seeds are a dramatic demonstration the Fibonacci Sequence in nature.

### The Importance of the Fibonacci Sequence

While this series of numbers from this simple brain teaser may seem inconsequential, it has been rediscovered in an astonishing variety of forms, from branches of advanced mathematics [5] to applications in computer science [6], statistics [7], nature [8], and agile development.

### How Τhe Fibonacci Sequence Ιs Used Ιn Agile Development

Now you may be saying to yourself “*That’s nice, but what does it have to do with Agile Development?*”, and that’s a great question. What does the Fibonacci Sequence have to do with Agile Development?**Interestingly, the Fibonacci’s Sequence is a useful tool for estimating the time to complete tasks.**

### Estimating Tasks In Agile

A big part of managing an Agile team is estimating the time tasks will take to complete. A points system is often used to give a high-level estimate of the scale or size of a specific task. Bigger more complex tasks get more points and smaller tasks get fewer points. Managers can then review and prioritize tasks based upon the assigned scale.

### Using The Fibonacci Sequence With Your Team

To use the Fibonacci Sequence, instruct your team to score tasks from the Fibonacci Sequence up to 21.

**1, 2, 3, 5, 8, 13, 21**

One being the smallest easiest tasks and twenty-one being large projects. As far as why you should use the Fibonacci sequence instead of, say, t-shirt sizes, check back for my next article on *5 Reasons Using the Fibonacci Sequence Will Make You Better at Estimating Tasks in Agile Development*.

And for more on leading an Agile eLearning Development team, check out our sweet eBook guide, The Agile Guide to Agile Development.

#### Related articles:

1.5 Reasons Using The Fibonacci Sequence Makes You Better At Agile Development

2.8 Components And Uses Of Burndown Charts In Agile Development

3. eBook: The Agile Guide To Agile Development

**References**

- Golden ratio
- Golden rectangle
- Leonardo Pisano Fibonacci
- Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation (Sources and Studies in the History of Mathematics and Physical Sciences)
- Fibonacci Sequence
- Why are Fibonacci numbers significant in computer science?
- Fibonacci Numbers, Statistical Convergence and Applications
- Fibonacci in Nature

## FAQs

### What is the Fibonacci sequence used for in Agile? ›

Essentially, the Agile Fibonacci scale **gives teams a more realistic way to approach estimates using story points**. Story points are used to represent the size, complexity, and effort needed for completing or implementing a user story.

**Why use modified Fibonacci sequence in Agile? ›**

The advantage of using the modified Fibonacci sequence is that **it is easy to use and understand**. This is especially important in SAFe Agile environments, where there is often a lot of uncertainty about the effort required for a task.

**What is the Fibonacci sequence explain its importance? ›**

Fibonacci Sequence Rule

**The golden ratio of 1.618, important to mathematicians, scientists, and naturalists for centuries is derived from the Fibonacci sequence**. The quotient between each successive pair of Fibonacci numbers in the sequence approximates 1.618, or its inverse 0.618.

**How is the Fibonacci sequence used in real life? ›**

The Fibonacci sequence can also be seen in the way **tree branches form or split**. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems.

**What is the Agile process sequence? ›**

It contains six phases: **concept, inception, iteration, release, maintenance, and retirement**. The Agile life cycle will vary slightly depending on the project management methodology chosen by a team. For example, Scrum teams work in short time periods known as sprints, which are similar to iterations.

**What are examples of Fibonacci sequence in design? ›**

A perfect example of this is the **nautilus shell**, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.

**What is the modified Fibonacci sequence in SAFe agile? ›**

A Modified Fibonacci Sequence is a relative estimating number sequence (1, 2, 3, 5, 8, 13, 20, 40, 100) that reflects the inherent uncertainty of the job being estimated.

**What is the modified Fibonacci sequence in scaled agile? ›**

' A modified Fibonacci sequence (**1, 2, 3, 5, 8, 13, 20, 40, 100**) [2] is applied that reflects the inherent uncertainty in estimating, especially large numbers (for example, 20, 40, 100).

**What is the advantage of Fibonacci? ›**

**Higher bandwidth means faster speed**

Fibre optic networks are significantly faster than even the highest-speed copper Internet connections, with options ranging from 5 Mbps to 100 Gbps. With a fibre optic network, your employees can benefit from equal upload and download times through a fast data connection.

**What is unique about the Fibonacci sequence? ›**

This is the Fibonacci Sequence. **It goes on infinitely and is made up of the series of numbers starting with 0, followed by 1, where each subsequent number is the sum of the previous two numbers**. November 23rd is Fibonacci day because when written in mm/dd format as 11/23, these four numbers form a Fibonacci sequence.

### What is the most important Fibonacci level? ›

The Fibonacci retracement levels are counted on these numbers. Each previous number amounts to approximately 61.8% of the following number, 38.2% of the number after, and 23.6% of the figure after that. The crucial Fibonacci retracement levels are **161.8%**, 61.8%, and 38.2%.

**What is Fibonacci sequence in simple words? ›**

The Fibonacci sequence is **a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers**. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.

**What are the 3 uses of Fibonacci sequence? ›**

Economics use the sequence very frequently, but so do optics. Nature makes frequent use of the system, sunflowers, artichokes and galaxies, even. Music uses the Golden Ratio and the sequence, and there is even a method of composing dedicated to the use of the sequence, the Schillinger System.

**How accurate is the Fibonacci sequence? ›**

How Accurate Are Fibonacci Retracements? Some experts believe that Fibonacci retracements can forecast **about 70% of market movements**, especially when a specific price point is predicted.

**What is the technique used for evaluating User Stories? ›**

**Top 5 User Story Estimation Techniques**

- Planning Poker. This method uses the Fibonacci sequence where user story point values are presented as 0, 1, 2, 3, 5, 8, 13, 20, 40, and 100 on playing cards, associated with different levels of complexity. ...
- T-shirt Size Estimation. ...
- Dot Voting. ...
- Bucket System. ...
- Affinity Mapping System.

**What are the story point values in Agile? ›**

Story points in Agile are **abstract measurements that developers use instead of hours**. Points are relative values, so a story with a value of four is twice as hard as a story with a value of two. The actual numbers don't matter — you could assign values between 1,000,000 and 5,000,000 if you want.

**How many hours is 1 story point? ›**

What do Story Points represent? Story Points represent the effort required to put a PBI (Product Backlog Item) live. Each Story Point represents a normal distribution of time. For example,1 Story Point could represent a range of **4–12 hours**, 2 Story Points 10–20 hours, and so on.