What is GOLDEN RATIO ? 
Golden Ratio is special irrational number represented by 'Φ' . Its value is around 1.61803398874989484820. If the ratio of two numbers turns out to be tending to 1.6180, then the numbers are said to be in Golden Ratio.
In mathematics, two quantities are said to be golden ratio, if their ratio is same as the ratio of their sum to the largest of the two quantities. Consider, two numbers 'a' and 'b', where a > b, their golden ratio is represented as,
a / b = (a + b) / a = Φ
It is the solution of the quadratic equation, x2 - x - 1 = 0 , that is x = (1 + √5) / 2
Did you know ? 
The ratios of sequential Fibonacci numbers ( 2/1 , 3/2 , 5/3 ... ) approach to the golden ratio. In fact, the higher the Fibonacci numbers, their ratio is closer to 1.6180339... . Here is a small illustration ,
2 / 1 = 2.00000
3 / 2 = 1.50000
5 / 3 = 1.66667
8 / 5 = 1.60000
The golden ratio is sometimes called the 'Divine Proportion', because of its frequency in the natural world.
Seems interesting right!! 
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Wonder where it's used ? 
Have you ever wondered why Apple's logo is so asthetic? Well, it is one among enormous applications of the concept of Golden Ratio.
The Golden Ratio is used by developers to design logos for their products. Logos of brands like Nike and Volkswagen are other classy examples of it. No suprise that the Golden Ratio was also used in various historical monuments since the beginning of human civilizations.
Click here to view more tempting applications of the Golden Ratio.