What is the Golden ratio?

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0,1, 1, 2, 3, 5, 8, 13…..

If you have read The Da Vinci Code by Dan Brown you would remember that this is a Fibonacci series. But what is actually common in Fibonacci series and your fingers or the tree branches or the sunflower ? Well, it the Golden Ratio!!!

Lets first understand this ratio. Consider a line, and divide into two parts such that the shorter length is that times of the larger length, as the larger length is to the whole line i.e the ratio of the shorter length to the larger length is equal to the ratio of the larger length to the whole line.

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This ratio is equal to 1.618 . And this ratio is also called as the Golden Ratio or the  Divine Proportion or the Golden Number. It is denoted by Greek letter Phi  [φ].

Strikingly, this ratio is also followed in human body. The ratio of your fingers, legs and even features of your face. The nature holds symmetry even what appears to us the most asymmetric. The growth of the branches, the arrangement of seeds in beautiful sunflower, the spirals of sea shell ( The Nautilus ), the converges of mighty hurricane and the galaxies etc are just few example to be noted.

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Mathematically, phi is an irrational number just like his more famous relative pi. That means that phi can’t be denoted in fractional form. Here are few interesting calculations related to phi.

1/phi= phi -1

phi2=phi+1

Also try it, 1.618 x 1.618 = 2.168. None of the other numbers holds such a beauty .

When Golden Ratio is followed in architectural landmarks such as

The Great Pyramids of Egypt

The Parthenon

Notre Dame Cathedral

Famous philosopher, scientist and artist Leonardo Da Vinci quite subtly embraced the beauty of the phi in his paintings Mona Lisa and The Last Supper .

The 17th century violinist Antonio Stradivari discovered that the 1st, 3rd , 5th and 8th (octave) numbers have a harmonious relationship.

A rational question arises in mind though, how is the Fibonacci series and the Golden Ration related?

The answer lies in the quotient

By dividing each of the successive term to the preceding term, the ratio remains close to 1.6.Lets check out –

5/3=1.666

8/5=1.600

13/8=1.625

21/13=1.615

34/21=1.619 and so on

 

Now you see the magic of this amazing number. Plotting the Fibonacci series number on a special graph, the Golden Spiral  is obtained , which is followed in all the above mentioned spirals.

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So you see, even the nature follows an intricate design in which all of us are carefully embroidered to form a beautiful masterpiece called the life. Look closely , and you would find it almost everywhere.