The Golden Ratio

The golden ratio is 1:1.618. We see that 1.618 is often represented as phi. The origin of the golden ratio is unknown. It is assumed that it has been discovered and rediscovered all throughout history. This would explain the different names such as the golden mean and phi. It is believed that the golden ratio has been used by the Egyptian when constructing the pyramids and by the Greeks when constructing the Parthenon.  Euclid linked this ratio to the pentagram as well.

What makes the golden ratio so interesting is many artists don’t know about it but continually will make it in their work. People seem to find pleasure in that specific ratio. Many people have created art, of all kinds, and not realized that their masterpiece consisted of the golden ratio. One example is Fibonacci numbers. They have a strong relationship with the golden ratio and it is believed that Leonardo Fibonacci didn’t even know it. It is know that Fivonacci’s sequence goes for infinitely long. If two consecutive numbers of the Fibonacci sequence are divided by each other, the further in the sequence the closer it to phi (1.618). If looking at the first ten numbers of the Fibonacci sequence we have 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55. If we divide the number next by the previous number we will start to move closer to phi. This is shown in the table below

First number (F­a)

Number Next (Fb)

Fb/Fa

1

1

1/1=1

1

2

2/1=2

2

3

3/2=1.5

3

5

5/3=1.667

5

8

8/5=1.6

8

13

13/8=1.625

13

21

21/13=1.615

21

34

34/21=1.619

34

55

55/34=1.6176

 

Basically f(x) = Fb/Fa approaches phi (1.6180339) as x goes to infinity. It is really funny that a mathematician would find a sequence of numbers that would be ground breaking stuff and within this amazing work lies another more subtle amazing creation. So that leave me and other with the question why is this golden ratio so loved by the human eye and occurs time and time again in history?   

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