Fibonacci Day 2024: Unravelling Nature’s Math

Every year on November 23, students worldwide celebrate Fibonacci Day, honouring the mathematical sequence discovered by the brilliant mathematician Leonardo Fibonacci. The day celebrates the sequence that starts with 0 and 1, where each subsequent number is the sum of the two preceding ones. This sequence, known as the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13…), appears in surprising places throughout nature.

According to Naresh Marwaha, HoD, Mathematics (Secondary Level) Apeejay School, Mahavir Marg, The Fibonacci sequence is defined by:

                                        1 = a₁ = a₂ and a_n = a_{(n – 1)} + a_{(n – 2)} , n > 2

“The sequence came from a puzzle about the rabbit population. This puzzle is mentioned in Leonardo’s book named Liber Abaci (a book on the Abacus). The puzzle was that if there are a pair of newly born rabbits male and female and they can produce another pair of rabbits in their second month of life then how many pairs of rabbits will be produced after a year? Leonardo Fibonacci was also responsible for generating the Hindu-Arabic numerals, popular in Europe,” the educator explained.

Exploring Nature’s Patterns

Nature is filled with examples of Fibonacci numbers, he added. “Did you know that the petals of a flower often follow the sequence of 3, 5, 8, or 13, and the spirals of a pinecone or the seeds of a sunflower also adhere to Fibonacci’s mathematical rule? These patterns not only showcase the elegance of mathematics but also illustrate how deeply intertwined Math is with the natural world,” Mr Marwaha said.

Beyond its natural occurrences, the Fibonacci sequence plays a crucial role in modern mathematics and various disciplines. It appears in Pascal’s Triangle, a key mathematical structure, and its ratios are fundamental to the concept of the golden ratio, found in art, architecture, and even music.

“When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio “φ” which is approximately 1.618034…”The bigger the pair of Fibonacci numbers, the closer the approximation! Even more surprising is that we can calculate any Fibonacci number using the Golden Ratio: Fn = (Φn – (1-Φ)n)/√5. The answer always comes out as a whole number, exactly equal to the addition of the previous two terms,” he said.

Fun Activity for the students

To celebrate Fibonacci Day, students can engage in hands-on activities. Here is a little exercise for the students: The list of first 20 terms in the Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, and 4181. Figure out the next few numbers…

The day is more than just a celebration of numbers; by exploring the Fibonacci sequence and its applications, students can cultivate a deeper appreciation for the patterns that surround us and the role mathematics plays in unravelling their mysteries.