The Golden Ratio

The Golden Ratio is a mathematical ratio. It is commonly found in nature, and when used in a design, it fosters organic and natural-looking compositions that are aesthetically pleasing to the eye. But what exactly is the Golden Ratio and how can you use it to improve your own designs.

In mathematics, 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. The figure on the right illustrates the geometric relationship.

Mathematically, If a/b = (a+b)/a, then a/b is said to be the Golden Ratio.  

It is often symbolized using phi (φ) and Phi = 1.68033988749894842O ...

It would be a surprise for most people to know that the golden ratio is often used to make attractive designs and logos.  Not only this, but already existing beautiful things in nature turn out to be in golden ratio!

Now considering the Fibonacci Series which goes by 1,1,2,3,5,8,13,21,34,55,89.... and so on. 

starting with 1and 1 as the first two numbers, each term is the sum of its previous two terms. 

if we consider b = 21, a = 34.  then a/b ≈1.618 ... which is nothing but phi ! 

now a+b = 55 which is the next term of the Fibonacci series, calculating (a+b)/a = 55/34 ≈ 1.618 ..

Hence except for the first 4 terms, all the terms of the Fibonacci series are in golden ratio  with their previous terms

The idea follows the observation that nature is full of patterns, such as the Fibonacci sequence, a series of numbers in which each number is the sum of the previous two numbers. The flowering of an artichoke follows this sequence, for example:-

                    just look around yourself ,there is  so many examples found in nature.

                                                that's the beauty of golden ratio

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                                                               thanks for reading

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