November 17, 2011

A Special Series - Fibonacci Series!

Hi Guys,

I hope all of you know about Fibonacci Series in mathematics. If not in math, all of you would have heard about this number while learning computer languages as writing a program to generate a Fibonacci Series (I learnt it this way from my brother 7-8 years back). For a few days, a video has been roaming in Facebook portraying the specialty of Fibonacci Series.

So, what is a Fibonacci Series? It was Leonardo of Pisa (who was known as Fibonacci) in 1202. The series is got by adding 0 and 1, followed by the result and the previous number.

0+1=1; 1+1=2; 1+2=3; 2+3=5…. The series is 0,1,1,2,3,5,8,13,21,34………..

Fibonacci Numbers also form Golden Ratio. Golden ratio is a set of very special numbers. Consider two quantities a,b (and a>b). If a+b:a is equal to a:b, then it is said to be Golden Ratio. All the Fibonacci Numbers are in such a ratio.

55/34 = 34/21 = 21/13 = 13/8 = 8/5 and so on.

A rectangle formed by two consecutive Fibonacci numbers is known as a perfect rectangle or golden rectangle. This rectangle can be divided into squares until the square of size 1*1 is formed.

A Fibonacci Spiral or Golden Spiral can be formed by connecting two ends of a square starting the 1*1 to the largest square.

So, what is special in this? We are able to find this spiral in lot of nature’s applications. A lot of medieval artists have used the Golden Ratio to construct the buildings or statues.

If you consider flowers, the petals are having Fibonacci Numbers. One and 2 petalled flowers are not common. Some flowers have 3 (lily), many have 5 (hibiscus, rose), some have 8. After that there are only 13, 21, 34,55… petalled flowers. It is interesting that these flowers have the same number of petals as found in a Fibonacci Series. Why is that there are no other number of petals? Similarly the head of sun flower, the cone of a pine tree, the diagonal of pine apple all have the same number as that corresponds to a number in Fibonacci Series.

One possible explanation given is that Fibonacci numbers fill the space effectively without leaving any gap. In any other pattern, spaces will be left, but in this type of pattern, there will be no spaces (see reference site for more details).

Human Hand is also said as an example. There are 5 fingers, divided into three parts separated by 3 knuckles (to me it appears as coincidence).

Common Shells have the same shape as that of a Fibonacci Spiral. Similarly Human Ear also has got a shape of Fibonacci Spiral. Similarly lot of other natural elements has got the shape of Fibonacci Spiral. Check the reference site to gather more information.

Some people say that as Fibonacci Series is found everywhere on Earth, it is a symbol of God and it is the unique touch of God. If these people want to prove that there is God, then I think they need not go too far. Everything in Earth is symmetrical. Isn’t that enough to say that God created everything in symmetry. If there is man, then there is woman. Heaven – Hell, Day – Night, summer – winter, etc. (just a reflection from Dan Brown’s Angels and Demons)

Happy Reading!!!



  1. I didn't know so many things about Fibonacci Series, thanks to you know I know them.
    As we discussed on twitter we Engineers all have tolled hard for it : )

  2. Thanks for sharing this bit of information , really interesting .

  3. nice information and dont know much about fibonacci before and the examples for it is also super

  4. Wow! Never knew so much about this series... Also try to find out about the number Phi, you will be amazed... Maybe we can have another article on it!!
    Have a nice day Karthick:)

  5. @all

    thanks for ur comments...

    yeah, its really amazing that fibonacci has lot of specialties...


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