Fibonacci Sequence

Fibonacci

Understanding the Fibonacci Sequence Through Python’s Recursion

The Fibonacci sequence is a fundamental concept in mathematics and computer science, often used to introduce beginners to the world of programming.

The sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … and so on. In this article, I’ll dissect a Python function that calculates the n-th Fibonacci number using recursion.

This code works by recursively calling the fibonacci() function to calculate the Fibonacci numbers of num - 1 and num - 2, and then adding those two numbers together.

1. The function takes one argument, num.
2. The function checks if num is equal to 0 or 1.
3. If num is equal to 0, the function returns 0.
4. If num is equal to 1, the function returns 1.
5. Otherwise, the function recursively calls itself to calculate the Fibonacci numbers of num - 1 and num - 2, and then adds those two numbers together.
6. The function returns the result of the addition.

def fibonacci(num):

This line defines a function called fibonacci(). The function takes one argument, num, and returns the Fibonacci number of num.

if num == 0:
    return 0

This line checks if num is equal to 0, the function immediately returns 0.

if num == 1:
    return 1

This line checks if num is equal to 1, the function immediately returns 1.

This is because the first two numbers in the Fibonacci sequence are 0 and 1, and all other numbers in the sequence are the sum of the two previous numbers.

return fibonacci(num - 1) + fibonacci(num - 2)

If num is neither 0 nor 1, the function calculates the n-th Fibonacci number as the sum of the (n-1)-th and (n-2)-th Fibonacci numbers.

This is done through two recursive function calls: fibonacci(num - 1) and fibonacci(num - 2).

print(fibonacci(7))

This line prints the Fibonacci number of 7.

Here is an example of the output of the code:

13

Applications of the Fibonacci Sequence

The Fibonacci sequence has many applications in mathematics, computer science, and other fields.

Some examples include:

• Mathematics: The Fibonacci sequence can be used to solve a variety of mathematical problems, such as calculating the probability of certain events or determining the optimal strategy for a game.
• Computer science: The Fibonacci sequence can be used to implement efficient algorithms for tasks such as sorting and searching.
• Finance: The Fibonacci sequence can be used to identify trends in stock prices and other financial data.
• Art and design: The Fibonacci sequence can be used to create aesthetically pleasing patterns and designs.

Conclusion

Recursive functions can be difficult to understand at first, but they can be a very powerful tool for solving problems.

The Fibonacci function is a good example of a problem that can be solved easily using recursion.

Here is the source code on GitHub :

Fibonacci