## Tuesday, February 3, 2009

Golden Ratio and Fibonacci Numbers

I got chance to read “ The De Vinci code” book last year, any one who had read the book will praise for its twist and turn and its code breaking scenarios which kept the reader interested. Among that thrill, suspense and murder the author introduces”Golden Ratio” to the reader.
I could not resist myself in doing a small research on Golden Ratio. The results were interesting, some times even suspicious. But it worth sharing and knowing about this will really enrich us.

If some one wants to write about Golden ratio he can keep on writing volumes and volumes of book. I like to make a short note on “Golden Ratio”.

The real intention of this article is to make people aware of the mere existence of the golden ratio and it is up to the readers to explore more. Lots and Lots of information are available in internet and I don’t want to duplicate that information here.

To understand Golden Ratio, first we need to understand Fibonacci sequence. The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. So a Fibonacci sequence will look like
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377……….

Ok

Now let us do some simple Mathematics. Take Ratio of the successive numbers of the Fibonacci sequence.

Numbers 1/0 1/1 2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 89/55 144/89 233/144 377/233
Ratio Infinity 1 2 1.5 1.667 1.6 1.625 1.615 1.619 1.618 1.618 1.618 1.618 1.618

Can you find that the ratio started with infinity had settled to a constant value of 1.618? In fact this is not a constant value, it is an irrational number same like our PI (3.142…..)

This ratio 1.618 is called Golden ratio.
Interesting thing about the Golden Ratio is the Application in various fields and existence in Nature. Golden ratio is being used right from Art, Literature, Music, Architecture, Aesthetics etc…….

If you search in net you will be amazed by the application and existence of golden ratio. I don’t want to write in this article as it is too time consuming and will make you to see only what I have seen and read.

Possible search tips are
1. Golden ratio and Human body.
2. Golden ratio and Nature.
3. Golden ratio. Etc…

This Golden Ratio is also called as Divine Proposition as most of nature grow or exist in a regular patter of golden ratio.
Even Human body display Golden ratio in each and every part of it.
Flowers, fruits, arrangement of seeds, growth of a plant, bacteria, etc….. Though it look like chaotic and structure less but the truth is there exist a fundamental pattern in which Nature works.

Another simple thing to do is next time if you see any thing or anybody aesthetic and beautiful or sounds very pleasant. Try to figure out the golden ratio in it. You will be thrilled and will start appreciating the Nature.

The rule is if the ratio is more closer to 1.618 we human fell that as more beautiful.

“My personnel opinion is that we love nature just because we love Golden ratio as golden ratio is every where in Nature even with in us “

If you want to make some thing beautiful apply Golden ratio. See the new High definition TVs,Plasma TV or LCD TV. it look beautiful and they say it will be pleasing to Eyes. Is the dimension of those TV are in GOlden ratio? I have not tried it, if some one can share after calculating.