What is the Fibonacci Sequence?

by Gauri (Upper Fourth)

1 March 2024

This article was written by Gauri (Upper Fourth) as part of the Pioneer, Edition 2. The Pioneer is a magazine packed with lots of exciting and interesting things to do and learn about STEM subjects – Science, Technology, Engineering and Maths; and a little bit about what it’s like to study STEM at Downe House.

The Fibonacci series is the sequence of numbers (also known as Fibonacci numbers), where every number is the sum of the previous two numbers. For example, the very first term is ‘0’ and ‘1.’ They get added together to make the next number in the sequence, which is ‘1’ in this case. Then, this answer (‘1’) is added to the number before that (‘1’ as well) and this makes the next number in the sequence (‘2’) … and so on. A Fibonacci series can thus be given as, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34….

The Fibonacci sequence was first invented by the Italian mathematician Leonardo Pisano, who is also known as Leonardo of Pisa. He discovered the Fibonacci sequence around 1200 A.D.. Leonardo Pisano Fibonacci was an Italian number theorist who also introduced the world to many mathematical concepts as what is now known as the Arabic numbering system, the concept of square roots, number sequencing, and even some math word problems.

In relation to the Fibonacci numbers, we also learn about the Fibonacci spiral. When drawing this spiral on a grid, you should first square the numbers in the Fibonacci sequence (from the beginning); for example, the squared numbers would be: 0, 1, 1, 4, 9, 25, 64, … These numbers each make their own little rectangle when you count and fit the squares on the grid side by side. Then, you must label the rectangle with the original number that was squared. This means that when you link the opposite corners with a curved line.

The Fibonacci sequence is also found in nature, reflecting various patterns. The sequence reflects the notion that nature is efficient yet “lazy,” making the most of available resources. Though it may seem strange, here are some mind-boggling facts. The Fibonacci numbers are always present in:

  • The proportions of the spiral on a Nautilus shell.
  • The arrangement of pinecones’ scales.
  • The branching of trees.
  • The total number of petals of a flower, as with irises and lilies.
  • Most pineapples have either five, eight, thirteen or twenty-one spirals; these are also Fibonacci numbers.
  • Romanesque broccoli, where each nub is a Fibonacci spiral of its own.

Fibonacci is so important, even today. This series, though invented in the twelfth or thirteenth century, is plainly still useful and still presenting avenues for sophisticated research such as some elements of nature. Fibonacci will continue to impact our lives all the time. What are the limits of Fibonacci?

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