# 1,1,2,3,5,8,13,21,34,55,89,144,233,377

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The golden ratio is an irrational number who discovered ancient scholars to warn the link between two segments belonging to the same line. This proportion can be found in nature (flowers, leaves, etc.) and geometric figures and given an aesthetic condition: that which forms respect the golden ratio is considered beautiful.

The golden ratio were studied since antiquity, as appears regularly in geometry. It is already known of its existence in regular and pentacles pentagons of Sumerian tablets from about 3200. B. C. In ancient Greece was used to establish the proportions of temples, both in plan and in their facades. At that time received no special name, as it was something so familiar among the ancient Greeks that “the division of a segment in extreme and mean ratio” was generally known as “the section“. In the Parthenon, Phidias also applied in the composition of the sculptures. (the name Phi, being the first letter of his name, made in 1900 the mathematician Mark Barr in his honor) .Platón, considered the golden section (ratio)  as the best of all mathematical relationships and the key to the physics of the cosmos. The golden section (ratio)  was widely used during the Renaissance, particularly in the visual arts and architecture. It was considered the perfect ratio between the sides of a rectangle.

Da Vinci made artwork for a dissertation published by Luca Paciolien 1509 entitled De Divina Proportione, perhaps the earliest reference in literature to another of his names, that of “Divine Proportion“. This book contains drawings by Leonardo da Vinci of the five Platonic solids. It was probably Leonardo who first gave the name of golden section. In 1525, Albrecht Dürer published Instruction on the measure with a ruler and compass plane and solid describing how to draw with ruler and compass the spiral based on the golden section, known as “spiral of Dürer”.

This ratio, which is also often mentioned as golden ratio, golden number or divine proportion, even used to be identified by their supposed mystical properties.

It can be said that the golden ratio comes from the relationship between a segment a and segment b. The a segment is longer than the segment b, while the total length of the line is, to the segment a as the segment a is to the segment b.

If we put the golden ratio in algebraic expression, we would have the following equation: (a + b) / a = a / b. The golden ratio, which is mentioned with the Greek letter phi, is the result of the division between a and b.

Another way to understand the concept of golden ratio is to find the following equivalence, also reflected in the above algebraic expression: if we take a segment and cut it in two, the quotient of dividing the length of the line (a + b) and the length of the longest segment (a) must equal the quotient of dividing the length of the longest segment (a) and length of the lower segment (b).

Although its definition resulting abstract and difficult to understand, the application of the golden ratio is important in photography, painting, sculpture and other arts that often link the beauty ideal symmetry and proportions

Being able to understand in a simple way, the Golden Ratio establishes that small is big as big is the whole. (As above, so below ; as below , so above- Hermes Trismegistus-)This usually applies to the proportions between segments. This ratio has been revered by every culture on this planet. We can find it in art, music composition, even in the proportions of our own bodies, and generally in all of Nature “hidden” behind the Fibonacci sequence. In mathematics, the Fibonacci sequence (sometimes wrongly called Fibonacci series) is the following infinite sequence of natural numbers:

1,1,2,3,5,8,13,21,34,55,89,144,233,377

The sequence begins with the numbers 1 and 1 and from these, “each term is the sum of the previous two” is the recurrence relation that defines it.

The elements of this sequence are called Fibonacci numbers. This sequence was described in Europe by Leonardo of Pisa, the thirteenth century Italian mathematician also known as Fibonacci. It has numerous applications in computer science, mathematics and game theory. It also appears in biological settings, such as in the branches of trees, in the arrangement of leaves on the stem, in the flora of the artichoke, broccoli inflorescences of romanescu and the arrangement of a cone.

The Golden number is a transcendental number. Transcendental numbers are real numbers that are not solving any rational polynomial coefficients. We could infer that irrational numbers are transcendental, but it is false. All transcendent are irrational; but not vice versa. Three of the most important numbers within that group are the number Pi, the number E and aureo number, known in mathematics by the name of Phi.

The relationship between the phalanges of the fingers is the golden ratio

The measurement of the length of the head and its width is also this issue

The ratio between full leg and knee height has that relationship.

The ratio between the whole arm below the elbow and has this relationship

And there are many more. Do you want to see a very conclusive proof?, for then look at the bottom ear. As can be seen, the human ear follows the same logarithmic of the spiral nautilus and this is nothing but the application of the golden ratio.

To conclude this part of the man must not forget Leonardo DaVinci, everyone knows your drawing called Vitruvius in which a man appears inside a pentagon. However, the relationship between the total height of the man and the distance between the navel and the tip of the hand are in this ratio. This article was written by Psalm Triginta yvanmcgregorFebruary 2, 2015 at 4:06 pmReply