Theory:

Nature is indeed a great wonder. We can understand everything around us through mathematics language.

The beautiful things in nature, as well as man, made things are connected with Mathematics. That is why there is a saying that "Mathematics is a nature's language".

In this lesson, we will get to know about a mathematics wonder, the Fibonacci numbers.
Fibonacci numbers
The term “Fibonacci numbers” describe the series of numbers generated by the below pattern.

$$0$$, $$1$$, $$1$$, $$2$$, $$3$$, $$5$$, $$8$$, $$13$$, $$21$$, $$34$$, $$55$$, $$89$$, $$144$$…,
Leonardo Bonacci is also known as Fibonacci, was an Italian mathematician who developed the Fibonacci Sequence. He discovered this fabulous sequence by the generations of rabbit breed.

Fibonacci sequence:
A sequence where the first two terms are $$0$$ and $$1$$, and each term, after that, is obtained by adding the two proceeding terms.
That is, the first two term of the Fibonacci sequence are $$0$$ and $$1$$. Adding this, we get a third term in the sequence $$0 + 1 = 1$$.

Next, adding the second and third term in the sequence, we get the fourth number $$1 + 1 = 2$$.

The below figure shows the pattern of the Fibonacci sequence.

[Note: Usually Fibonacci sequence start with $$1$$ not with $$0$$.]

We can observe that the fourth term of the Fibonacci sequence is the sum of the third term and the second term.

Therefore, we can form a generalized equation to obtain the Fibonacci number.

That is, $$F(n)= F(n–1) + F(n–2)$$.

Where $$F(n)$$ is the $$n^t$$$$^h$$ term.

$$F(n–1)$$ is the previous term to the $$n^t$$$$^h$$ term.

$$F(n–2)$$ is the term before the $$(n-1)^t$$$$^h$$ term.

Now, when $$n = 5$$, we can find the next Fibonacci number as follows.

$$F(5) = F(5–1) + F(5–2)$$

$$F(5) = F(4) + F(3)$$

$$F(5) = F(4) + F(3)$$

$$F(5) = 2 + 3 = 5$$.

Hence, using this formula, we can obtain any Fibonacci number.

In the upcoming lessons, we dive into the Fibonacci number's real-life examples to get a broad understanding.