2009-01-05

Italian mathematician **Leonardo Pisano **had a problem worked on to find a mathematical pattern to answer the question: how many pairs of rabbits can be produced from a single pair of rabbits in one year?

He carried out his work on following assumptions:

- Rabbits are kept under optimal conditions
- Female rabbits always give birth to pairs
- Each pair consists of one male and one female

If we start with a pair of new born rabbits and monitor the population monthly…

Rabbits cannot reproduce until they are at least one month old. So in the first month there will only be one pair and at the end of the second month the pair is able to reproduce so the female rabbit will give birth to a new pair.

In month three the original pair gives birth to yet another pair while their first pair of baby rabbits grows to the adulthood.

In the beginning of month four there are two pairs of adult rabbits and one pair growing so both of these adult pairs give birth to two new pairs. So the total number of pairs in the end of the fourth month:

Adult pairs : 2

Growing pairs : 3

Total : 5

Like wise the pattern goes on as follows:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … on to the infinity. Each number is the sum of the previous two.

**Leonardo Pisano **found this interesting pattern on 1202. How come the pattern is named Fibonacci Sequence?

**Leonardo Pisano **was also knows as ** Fibonacci, **meaning “son of Bonacci” giving this name to his finding.

**Are rabbits the only species having relevance to Fibonacci Sequence?**

Many natural entities such as Fruits, Vegetables and Seed Heads show spiral patterns which follows Fibonacci Sequence.

**Some examples:**

If you look at the array of seeds in a center of a sunflower you should notice that those seeds are arranged in spiral patterns curving left and right. And the amazing thing is if you count the number of these spirals you will get a Fibonacci number. The most amazing thing is if you divide the spirals pointed to left and right and count those separately you will get two consecutive Fibonacci numbers!

If you look at a pineapple you can notice that its scales make a spiral pattern and if you look closer and count those scales in each spiral you will notice that those numbers reflect Fibonacci Sequence.

Same thing can be noticed in pinecones, cauliflower and many more natural things we live with.

This sequence has an amazing link with the nature and that’s may be why the ratio between two of these numbers is called **The Golden Ratio**.

**The Golden Ratio**:

Two numbers are considered as in The Golden Ratio if the ratio between the sum of two numbers and the larger one is equal to the ratio between the larger one and the smaller.

In mathematics the golden ratio is often denoted by the Greek letter *ϕ (phi).*

*The value of the golden ratio: **ϕ** = 1.6180339887…*

Was this post helpful to you? How can I improve? – Your comment is highly appreciated!

Cassian Menol Razeek

It’s an interesting topic, good work.

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