GOLDEN RATIO IN ARCHITECTURE

There are many article about golden ratio & if you are in mathematics or architecture or botany you must have heard this word "Golden Ratio" so many times. & Also you must know its value

φ = 1.618033...

But very few knew about it. that how that ratio was derived.

There is so many calculation about it. 

Two quantities a and b are said to be in the golden ratio φ if

${\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi .}$

One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,

${\displaystyle {\frac {a+b}{a}}=1+{\frac {b}{a}}=1+{\frac {1}{\varphi }}.}$

Therefore,

${\displaystyle 1+{\frac {1}{\varphi }}=\varphi .}$

Multiplying by φ gives

${\displaystyle \varphi +1=\varphi ^{2}}$

which can be rearranged to

${\displaystyle {\varphi }^{2}-\varphi -1=0.}$

Using the quadratic formula, two solutions are obtained:

${\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }$

and

${\displaystyle \varphi ={\frac {1-{\sqrt {5}}}{2}}=-0.6180\,339887\dots }$

Because φ is the ratio between positive quantities φ is necessarily positive:

${\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots }$

but these all are depends up on a chain of number we all knew about it. but some of us didn't know that Fibonacci Series helps them to find golden ratio.

lets understand this..

series starts with 1,1,2,3,5,8,13,21,34,55,89,144,...

If you start taking ratio of each number with previous number. the result will be...

and if you draw a graph of it...

from point 5 to any point to right if you can take an average of the number you will find something like this φ = 1.618033...

Now, you must thinking where is architecture in it?

here you go..

This specific ratio or Fibonacci series has derived Golden Rectangle.

that's the principle on which there is so many building have been designed. so many elevation have been created. even lots of Famous Architects has follow this principle in their most famous building. 

i.e.,  Villa Stein, designed by Le Corbusier, was built in 1927 at Garches, France. lets see some of his work...

 even he has design furniture too on the principle of golden ratio.

there is few more building which follows the same principle of golden ratio...

I hope that you like the article. please for suggestion & query please comment below.

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