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#### Math Tutor – Fibonacci Numbers and Their Existence in Nature # Math Tutor

## Fibonacci Numbers and Their Existence in Nature

Credit for having formed the Fibonacci Numbers belongs to an Italian mathematician named Leonardo Pisano who coined them for the first time in 1202 after having observed the breeding of rabbits.

How did Fibonacci Numbers come into being?
As a mathematician, Leonardo Pisano found himself wondering how many rabbits could be produced within a time-frame of one year from a single pair of rabbits, assuming that all conditions were optimized. His experiment started with one pair of rabbits – a male and a female – and was based on the fact that rabbits take one month to mature sufficiently to be able to reproduce.

Over the first month there was only one pair and at the end of second month the female had given birth to the second pair, thus taking the total to four. At the end of the third month, another pair was born and by this time, the second pair was now ready to reproduce. So after four months, two pairs gave birth to two new pairs while the third attained maturity.

What you are bound to realize on following this sequence is that from the third number onward, every number is the sum of the two immediately preceding it. This pattern of numbers was termed as Fibonacci Numbers and it can continue till infinity.

Have you observed Fibonacci Numbers in nature?
It is not as if Fibonacci Numbers dominate the natural world around us, but they do dictate the sequence in several aspects of nature, some of which are as follows –

Fruits, vegetables and seeds – Among fruits, the markings on a pineapple reflect the Fibonacci Sequence and so do the ridges on the surface of a cauliflower. Pinecones also follow this pattern as do the seeds that are collected in the middle of a sunflower wherein they curve from left to right in a spiral pattern and on being divided and added, they form the Fibonacci number sequence.

Honeybee family tree – In a honeybee colony, there is the queen bee, the workers which are usually female bees and drones that emerge from unfertilized eggs. So while the worker bees have 2 parents, namely the queen bee and the drone, the drone has only one parent. This is where the Fibonacci Sequence comes in – the drone has one parent but two grandparents and three great grandparents and so on.

Human body – Most segments in the human body are one, two, three or five. For example, you have one nose, two hands, three parts in each limb and five digits on each of your hands and feet. Likewise, the proportion between segments also follows a certain ratio, namely the Golden Ratio, which is also regarded as being a derivative of Fibonacci Numbers.

Plants – In plants, the Fibonacci Sequence is visible at growth points, namely points at which branches of the tree split from the main trunk. From one trunk, there is one bifurcation which goes on the bifurcate further into two branches and then the main trunk sprouts another growth point, taking the number of points to three. Then the first growth point bifurcates into two growth points, taking the figure to five and in this way the sequence continues.

Final Word
Whether the presence of Fibonacci Numbers/Sequence in nature is a coincidence or by design is something that the scientists have failed to figure out till date. The only valid explanation is that maybe it is most effective as a survival tactic and hence has evolved over the generations.

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