Magical Golden Ratio

I have picked a beautiful topic today

The Golden Ratio

I bet only some of you might have heard about it and rarely anyone known it in detail.

If you want to know the ^so-called^ definition then here it is :

" Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. "

Okay okay, I understood that you didn't understand a word now :D

If you want to practically experience it then here I go ^_^


Anyone heard about Fibonacci series !?
Mostly those who prepared for Entrance/ competitive exams and Programmers must have heard about it.

The series looks like 1,1,2,3,5,8,13...


Here the Java program to generate Fibonacci series(Just for reference(Don't scold me :P)) :

class FibonacciExample1{  
public static void main(String args[])  
{    
 int n1=1,n2=1,n3,i,count=10;    
 System.out.print(n1+" "+n2);//printing 1 and 1    
    
 for(i=2;i//loop starts from 2 because 1's are already printed    
 {    
  n3=n1+n2;    
  System.out.print(" "+n3);    
  n1=n2;    
  n2=n3;     

    }

  }

}  

You might be wondering as what is the relation between these two ?

Look at the below picture :

The Golden Ratio is found by dividing a line into two parts.

The longer part divided by the smaller part is also equal to the whole length divided by the longer part.

Here

• The Longer part is a 
• The smaller part is b
• Whole length is a+b

(phi) = 1.6180339887498948420 … 

• Many buildings and artworks have the Golden Ratio in them.

The Golden ratio also appears in all forms of nature and science. Some unexpected places include:

Flower petals: The number of petals on some flowers follows the Fibonacci sequence.

Seed heads: The seeds of a flower are often produced at the center and migrate outward to fill the space. For example, sunflowers follow this pattern.

Shells: Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.

Let's stop here today :)

Tomorrow next part will be continued...

Thank you for your patience and interest....See ya