The golden ratio

The golden ratio ancient and medieval mathematics was called "divine proportion". Golden ratio is currently descended from Olympian heights in ordinary textbooks.

The golden ratio ancient and medieval mathematics was called divine proportion

However, in addition, that the golden ratio is known from textbooks, something else can be said about it.

The golden section of the segment a is expressed in two words, as follows: the whole segment of attitude toward the most part, as most of the to smaller. Hence the proportion of:

a : x = x : (a x).

This ratio gives an equation of the second degree:

x² + ax a² = 0.

This yields x/a golden ratio as the number 0,61804...

In ancient literature the golden ratio was first mentioned in the "Elements" of Euclid (300 BC), Where it is used for the construction of a regular pentagon. Luca Pacioli, a contemporary and friend of Leonardo da Vinci called this attitude "divine proportion". The term "golden ratio" was introduced in 1835 by Martin Ohm.

In the regular five-pointed star, each segment is divided crossing its segment in the golden ratio. The proportions of the Cheops pyramid, temples, bas-reliefs, household items and jewelry from the tomb of Tutankhamun show that Egyptian craftsmen used the ratios of the golden ratio in their creation.

The ratio of the lengths of parts of the human body, which is also often credited with the proportions of the golden ratio, in most cases differ from such.