The Golden Ratio

• In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.
• The Golden ratio is a special ratio. Phi (lowercase) is used to refer to this ratio, and the value is , which is approximately 1.618.
  The uppercase phi () is used for the reciprocal of the golden ratio, which is 1/.
  

• There are many different ways in which the Fibonacci sequence is related to the Golden Ratio. Firstly, the further you go to the right of the sequence, the more the ratio of one term to the one before it estimates the Golden Ratio. The table below shows the first few numbers and their ratios:

First number	Second number	Ratio
0	1	-
1	1	1.0000
1	2	2.0000
2	3	1.5000
3	5	1.6667
5	8	1.6000
8	13	1.6250
13	21	1.6154
21	34	1.6190
34	55	1.6176
55	89	1.6182
89	144	1.6180

 

• The golden ratio also determines how attractive a person is.
  For example, the American pop singer and actress Jessica Simpson is attractive because the proportion of her face fits geometrically on the human face mask which conforms to some aspect of the Golden Ratio.
  

• Do you think the Golden Ratio "naturally" occurs in nature and art/architecture or do people "force" it to be there?

Obviously, nature doesn't know about the golden ratio, but for art and architecture, which are created by people, in order to look "good" and well proportioned, yes they "force" it to be there.