Fibonacci Series: Meaning, Formula, Example, Golden Ratio

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fibonacci series

The Fibonacci Series is a popular sequence that is named after Leonardo Pisano Bogollo, an Italian Mathematician. However, its application is not limited to the world of mathematics only. Instead, it extends beyond the mathematical sphere to other aspects of our lives such as finance, music, engineering, cryptography, and the animal world as well. In this blog, we will explore the amusing details of the Fibonacci series or Fibonacci sequence, its formula, and how it has uses in diverse fields. Let’s begin with the basics first.

Source: MacTutor 

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What is Called the Fibonacci Series?

Source: TED

In layman’s language, the Fibonacci Series is an arrangement of numbers which is also referred to as the Fibonacci numbers. To understand this specific pattern of numbers, imagine a special arrangement of numbers where each number is created by simply adding the two numbers before it. This sequence begins with 0 and 1 and continues like  0, 1, 1, 2, 3, 5, 8….Here you can easily spot that you can calculate the next number by adding the two previous numbers. For example, to find the 6th number in a Fibonacci sequence, you just have to add the 4th and 5th numbers.

To make things simpler, let us assume that the first term F0 is 0 and the second term F1 is 1, here is how to find the third term:

F2= F0 + F1

F2= 1

Similarly, you can find the other terms of the series by simply applying the above-mentioned concept. 

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Fibonacci Series Formula

Fibonacci Series
Source: Medium

As you can see, the Fibonacci series formula can be used to calculate and find the missing terms or numbers in the series. The most common way to do that is by completing the Fibonacci series using recursion such that the Fn term can be found by simply adding the preceding two terms. 

Fn = Fn-1 + Fn-2,

where n > 1

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What is the Fibonacci Spiral?

The Fibonacci series in nature is an amusing concept to understand. The Fibonacci spiral is a mathematical pattern that intricately bears a resemblance to a swirling curve. To create this logarithmic spiral, the corners of squares that have side lengths corresponding to the numbers in a specific Fibonacci sequence are connected.  

logarithmic spiral that is simply formed by joining the corners of squares that have side lengths the same as the numbers in a specific Fibonacci sequence. This spiral makes frequent appearances in nature, especially in the arrangement of seeds in sunflowers, leaves on a stem, the shell of a nautilus, the galaxies, and so on.  


Below we have jotted down the numerous applications of the Fibonacci series. Let’s take a look at them one by one:

  • The Fibonacci series can be used in engineering such as data structures, sorting algorithms, trading algorithms, etc.
  • It is also used in music to create melodies and musical patterns. 
  • It can be used to create mathematically precise yet beautiful and captivating paintings and sculptures.
  • Biomimicry is another application of the Fibonacci series where engineers learn to create efficient products using patterns and arrangements found in nature. 

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Fibonacci Series Golden Ratio

Did you know that the Fibonacci Series is closely related to the value of the Golden Ratio? How? Well, to begin with, we already know that the value of the Golden Ratio is approximately 1.618034. Moreover, it is represented by using the ϕ symbol. So, if we take the ratio of two successive Fibonacci numbers (of bigger value) in a series, the ratio will be close to the Golden Ratio. 

For instance, the ratio of 34 and 21 is:

34/21 = 1.619

In the same way, you can find the Fibonacci numbers using the Golden Ratio. For that, here is the formula:

Xn = [φn – (1-φ)n]/√5

Symbol Description  
φ It is the Golden Ratio which is equal to 1.618 approximately. 
nThe nth term of a Fibonacci sequence. 

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What are the first 20 Fibonacci series?

The first 20 terms in the Fibonacci series are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181.

What is the sequence 1 1 2 3 5 8?

1 1 2 3 5 8 is the Fibonacci series in which a number can be easily found by simply adding the two numbers before it. 

How do you solve a Fibonacci sequence?

To solve a Fibonacci sequence, you can use the Fn = Fn-1 + Fn-2 formula where n is greater than 1. 

This blog was all about the Fibonacci series. For more information about such informative articles, make sure to check the trending events page of Leverage Edu.

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