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The golden number or phi is the relation or
portion there are between two segments of straight. Can be found not only in
geometric figures, if not also in the nature. It’s possible to find this
relation in a many works of architecture or in art. For example, “El Hombre de
Vitruvio”, drawn by Leonardo Da Vinci and considered a beauty ideal, is
proportionate according to the golden number.
The first to make a formal study of the
golden number was Euclides, about three centuries before Christ, in his work “Los
Elementos”. Euclides defined its worth saying that “one straight line is
divided in the entire line it’s to the mayor segment as the major is to the
minor”. In the other words, two positive numbers a and b are in golden
relation if and only if (a+b) / a= a/b. the valour of this number is irrational
and it has an infinite decimal, its approximate worth is 1’6180339887498…
The golden number also is “related” with
Fibonacci series. The golden number and Fibonacci series are continuously in
the structure of the living creatures. The phi number, for example, relates the
amount of male bees and female bees are in the hive, or the disposition of the
flower petals. The relationship between the Fibonacci sequence and the golden
number is the following:
1:1 = 1
2:1 = 2
3:2 = 1’5
5:3 = 1’66666666
8:5 = 1’6
13:8 = 1’625
21:13 = 1’6153846…
34:21 = 1’6190476…
55:34 = 1’ 6176471…
89:55 = 1’6181818…
To take more terms of the succession and
make it quotient, we approach to the golden number. When the terms increased,
the quotients approach to phi: 1’6180339887498…
1 comentarios:
As you mention the Fibonacci series and we are now studying series I would like to add some of the its first numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
They are generated following this function:
fn=f(n-1)+f(n-2)
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