Fibonacci Sequence
- toinfinityandbeyondmathclub
- Dec 4, 2021
- 2 min read
Updated: May 18, 2023
Have you ever looked up at the sky and noticed a particular fluffy cloud that's shaped like a tortoise, or have you observed that the craters on the moon seem to be arranged in the shape of a rabbit? Us humans have a tendency to notice familiar shapes and patterns that don’t always exist. This is called apophenia.
One of the most famous manifestations of this tendency is the Golden Ratio, derived from the Fibonacci sequence. From the Nautilus seashell to Leonardo da Vinci’s ‘Vitruvian Man’, from the pyramids at Giza to the Parthenon, people see the Golden Ratio in the proportions of architecture, art and nature. As it turns out, these are all myths according to Keith Devlin, a mathematician at Stanford University.
Though it may not be nature’s universal rule for designing the shapes of seashells, hurricanes and human body proportions, the Fibonacci Sequence is a fascinating piece of mathematics, so let us learn more about it and where it can actually be seen in nature.
The Fibonacci Sequence is one of the most famous formulas in Mathematics; it is a sequence of numbers where each number is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical equation describing it is Xn+2= Xn+1 + Xn
The Fibonacci sequence was understood in ancient Sanskrit texts centuries before it was named Fibonacci; as early as 200 BC, work by Pingala mentioned patterns of Sanskrit poetry formed from syllables of two lengths. However, outside of India, the sequence first appeared in 1202, in the book Liber Abaci (Book of Calculation) by Fibonacci, an Italian mathematician from the Republic of Pisa. Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci Sequence. Although rabbits don’t actually reproduce like this, the sequence does seem to capture some aspects of growth. We can notice Fibonacci numbers in biological setting such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts. The sequence can also be applied to computer algorithms sch as the Fibonacci search technique (a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers), and the Fibonacci heap data structure ( a data structure for priority queue operations).
So, while it may not be the code to crack the universe’s design, the Fibonacci Sequence is simple and poetic, the way the best Mathematic formulas are.
- Tamanna Balachandran
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