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Jurate Macnoriute
The Golden Proportion in Art and Nature

Long ago I started research in qualities of the golden proportion putting it into practice of painting. In 1994 I officially represented my ideas for professors of Vilnius art academy. In the beginning of 1995 I completed my little book The Golden Ratio in Art (terms golden proportion, golden ratio, golden section used in the text have this same meaning). Now time came to revise earlier research.

A lot of researchers starting from ancient Egyptians paid attention to proportion of the golden section. The golden section is the way of dividing a segment into two parts that ratio between larger part and all segment are equal to ratio between smaller part and larger; it has value 1.61803…

Russian architect I.Sh.Shevelev came to conclusion that the golden proportion (1 : 0.618...) or square root from 5 are characteristic for animate nature and for growth, and square root from 2 is found out in the descriptions of crystals' structure. R.Knott argues similarly. He proves that the golden section is the best arrangement of objects to minimize wasted space.

Let us go further and clear up such problems:
1. An object of animate nature and its coordination with proportional grids of the golden section and equal rectangles;
2. Relation between an object of animate nature and art work.

Ascertaining difference between an object of nature covered with grid of the golden section and grid of equal rectangles applying comparative and grids' methods I did such experiment. The first leaf of a plant which happens to find in a garden was photographed, and this photo was studied with the help of CorelDraw (Fig.1-2). The leaf was circumscribed into rectangle, on them grid constructed according with the golden proportion (Fig.1).

Fig.1 Fig.2

In Fig. 2 we see the same leaf with grid of equal rectangles dividing sides into 18 parts. It was found that 8.92% of lines' intersections are common, coordinated. Other grids of equal rectangles were also tested. Percentage of intersections with grid dividing sides into 32 parts is equal 8.05; into 40 parts equal 11.54. These results show that grid constructed according to the golden section is about three times more coordinated with the object of animate nature, than grids of equal rectangles.

As it is known Egyptians used square grids for formation of canonical proportions. They used proportion of the golden section too though it is not known from what time. Proportions of equal rectangles are easily noticed in fabrics when different colours' threads of the same thickness form ornaments. Thus the beginning of such grids' use was born together with fabrics. It is logicality that human being could discover the proportion of the golden section more later, because it is not related with the urgent matter of human existence, but with developed abstract mathematical mind. Thus we can affirm that proportions of equal parts as simplest are characteristic for human mind though, on the other hand, it is known that human brain and hearth work in rhythm of the golden section.

This hypothesis can be proved in not complicated way. For this I took my little drawing from very early period Fig.4 as most simple and examined it with the help of these same grids with which the leaf was examined. Only coordination of drawing's lines with horizontals of grids was taken into consideration. For better evidence the result of research is placed in the table below.

Fig.4

 Coordination of object and grid of the golden section Coordination of object and grid of equal rectangles which divides sides into 18 parts Coordination of object and grid of equal rectangles which divides sides into 32 parts Coordination of object and grid of equal rectangles which divides sides into 40 parts the example of animate nature (the leaf) 27,47% 8,92% 8,05% 11,54% the human drawing 67,65% 82,35% 80,64% 66,66%

These measurements were not homogeneous. Only main vein of the leaf was taken for the research of animate nature and all drawing for the second example. Therefore we can not compare these two results entirely, but general regularity can be noticed. If the object of animate nature is more coordinated with grid of the golden section, in the second case the coordination of human creation with all these grids more similar among themselves and even the percentage of some grids of equal rectangles many more exceed the data of the golden section. One shall say that we can not judge by one example, maybe my drawings are exception. But let us remember my earlier research. For instance, almost all details of Leonardo da Vinci's St. Jeronim touch the lines of grids of equal rectangles which divide picture's sides into 23, 24, 25, 32 parts. We can affirm that proportions of equal parts are characteristic for human mind and not characteristic for animate nature; that golden section grid is characteristic for human mind and for animate nature. If the golden section proportion gives to art work such properties of animated nature, as liveliness, not heaviness, unrest, then the proportions of equal parts would have to turn over reverse properties, as immobility, heaviness, stability. In any art work some balance exists of manifestation of these two oppositions.

The golden section is characteristic for human mind and for objects of animate nature; proportional grids of equal rectangles characteristic for human mind and not characteristic for objects of animate nature. Golden section proportion gives to art work such properties of animated nature, as liveliness, lightness; grids of equal rectangles stability and weight.

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