THE GOLDEN RATIO

The Golden ratio is an unique number in mathematics and its appearance can be found through out the different aspects of the nature: the human body, flowers, animals, fibonacci series, astronomy. arts, architecture and so on.

The golden number is an irrational number, represented by the Greek letter φ or Φ in honor of the Greek sculptor Phidias who used the golden ratio in the construction of the Parthenon. The equation is expressed as follows:

As it is mentioned before, the Golden ratio is present in everything around us, so I would like to show you some examples of it.

1. The Fibonacci series

The Fibonacci series is an infinite succession of natural numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21,... The first two numbers of the succession are 0 and 1. The other terms are the sum of the 2 previous terms in succession: 0+1 = 1, 1+1 = 2, 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13...

This succession we owe it to Leonardo of Pisa, also known as Fibonacci, who was an Italian mathematician of the XIII century. The succession can be found in the computing, mathematics, games, music and even in nature! According to Fibonacci series and Golden ratio, we can find the golden rectangle is a rectangle whose sides are in the golden reason. To construct a golden rectangle from a square side AB, just determine the midpoint M of one side AB, and draw, with center at point M, a circumference that passes through one of the vertices C on the opposite side. 

The incredible thing of the Golden rectangle is that it has occupied in architecture, like the Pyramids of Egypt, or also in design, as in credit cards, packets of tobacco and so on. This is not a coincidence because the Golden ratio represents beauty and balance, therefore our subconscious "fells in love" with these objects.

2. Nature

The Golden rectangle provides several examples in the nature. This shape can result in a process of imbrication that can be repeated infinitely, and takes the form of a spiral. It is called the logarithmic spiral, and it abundances in nature. For example, we can identify this logarithmic spiral in snail shells and nautilus shells and in spiral galaxies. 

3. Human face and body

It turns out that the quotient between the height of the man and the distance from the navel to the tip of the hand is the golden ratio. The most striking perhaps is the relative to the navel: if you divide the total height of a human between the distance from the navel to the feet we obtain the golden number. Moreover, in some recent studies, scientists have discovered that the teeth are growing according to the golden ratio. 

As I mentioned before in the section 1, sometimes we tend to fall in love of beauty people and it is due to the physical features that they have and it is quite relate with the relation between this and the golden ratio. I would like to share two table about superstars who have the most balanced face and body according to the proportions of the golden ratio.

         

WOMEN	%
Scarlett Johansson	96.4%
Kim Kardashian	96.3%
Helen Mirren	95.6%
Marilyn Monroe	94%
Rita Ora	93%
Kelly Brook	92.9%
Katy Perry	92%
Cameron Diaz	91%
Elle MacPherson	88.3%
Salma Hayek	88%

4. DNA molecules
Even the microscopic realm is not immune to Golden ratio. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each complete cycle of its double helix spiral. These numbers, 34 and 21, are part of the Fibonacci series, and their relationship 1.6190476 is very close to φ = 1.6180339.

5. Monuments