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Proportions of bodies.
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Principles of global harmony are determined by simple geometrical figures,
one of which is the heptagon and the heptagonal geometrical network of lines
which turns out if tops of the heptagon are connected by lines.
It is possible to assert that the heptagonal network is a basic figure which
determines harmonious proportions of world around.
The additional information on a heptagonal geometrical network of lines look in
other section of this website in concepts of the
Japanese garden of stones where proportions of a heptagon are compared
to rules of an arrangement of stones.
Including the heptagonal network of lines is a figure which determines proportions of a human body that is
shown on the chart:
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Dark contours in the chart show an ideal human figure
which is entered in lines of the heptagonal network. The shown figure is female (about proportions of an ideal male figure it is told further). Growth of a human body shares on 8 parts according to the ancient Greek sculptural canon and the size of a head makes 1/8 part from growth of a body that is shown in the chart by blue lines. Though actually the size of a head makes 1/8 part if growth of a man is 180 centimeters, but if growth of a man is 175 centimeters then the size of a head makes 1/7,5 part, or if growth of a man is 170 centimeters then the size of a head makes approximately 1/7 part according to the average anthropometrical measures. But however it is considered that the ideal size of a head corresponds to the Greek sculptural canon. It is necessary to tell that the ancient Greek canon for proportions of a human body was not kept, namely only a few phrases were kept but in essence the contents of this canon is not known. And also it is necessary to tell that in ancient Greek sources of the information there are no data on ratio of forms of a human body with lines of a heptagon, but however the heptagon is a basic geometrical figure which corresponds with forms of human bodies and proportions of the Greek sculptures. |
The shown figure can be used as a pattern which allows to draw ideal
proportions of a female body. Namely this pattern allows to measure lines of hips
and also waist and shoulders which are
the basic contours of a body and consequently the shown pattern is elementary
model which can be used for measurements of key parameters of an ideal body.
To measure detailed parameters of other lines of a body it is necessary to have
more complex pattern which is constructed in lines of the diheptagonal network
(fourteen-polygonal network), or it is necessary to use lines of the triheptagonal or the quadraheptagonal
networks which are more complex but allow to measure lines of hands and legs,
and also other forms not only female but also male bodies. That is possible to
see in following chart where the diheptagonal network corresponds with ideal
patterns of a female and a male body. And also it is possible to see in
galleries on pages of this website where some drawings represent figures of
human bodies which are constructed according to lines of triheptagonal and quadraheptagonal
networks.
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The female figure is shown by grey
contours and the male figure is shown by green contours in the chart. The diheptagonal network allows to describe the greater number of proportional points of a human body than the heptagonal network allows, and if to use triheptagonal or quadraheptagonal networks then proportional forms of human bodies can be described in detail enough. |
If to look at the figure of a female body then it is possible to see that
crossing of lines EJ and FK corresponds to knee joints, and crossing of lines AH
and DL corresponds to the umbilicus. Also in crossings of other lines it is
possible to find proportional points of a human body.
The male figure is generated from crossings of other lines rather than the
figure of a female body, but both figures correspond with lines of the diheptagonal
network. But it is necessary to consider that proportions of a male and a female
bodies have the ratio 15/14 (exact geometrical data 528/472) according to
statistical anthropometrical data. Namely if average growth of a man is 150
centimeters then average growth of a woman is 140 centimeters. Or if average
growth of a man is 176 centimeters then average growth of a woman is 164
centimeters that corresponds to average anthropometrical measurements.
Therefore it is necessary to transform the diheptagonal network that figures of
human bodies in lines could be according to the valid proportions that is shown
in following chart:
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In this chart the diheptagonal network of lines is
entered in frameworks of "living circle" in which the ratio of vertical
and horizontal diameters is approximately 15 /14 that is coordinated
with proportional ratio of a male and a female bodies. In essence this chart shows the ellipse (oval) in which the long axis corresponds to proportions of a male body and the short axis corresponds to proportions of a female body, but provided that angular position of male and female figures within the diheptagonal network is 360/14= 25,714x3=77,143 degrees that deforms proportions of a female figure. If to use the quadraheptagonal network of lines then patterns of a male and a female bodies can have the angular position 90 degrees and then proportions of figures have no distortions. The shown ellipse can be named "living circle" as such term is used in geometry for a definition of the living square with the attitude of the sides 15/14. |
The shown geometrical patterns of human bodies are approximate, but can be
used for exact calculations. If exact calculations of the sizes and proportions
are not actual then it is possible to use approximate patterns which are
sufficient for the fine arts.
I do not bring exact geometrical calculations as for this purpose it is
necessary to use mathematical formulas that is inexpedient in a context of the
present gallery of phantom images, but exact calculations can be executed
according to the submitted geometrical concepts.
The additional information on the sizes and proportions of a human body for exact calculations look in other sources of the information.
I should tell that the presented geometrical concepts of ideal proportions of a
human body are before not known, but I approve that the presented researches
correspond with principles of world harmony.
The following page considers proportions of the Egyptian Pyramids which correspond with proportions of a human body and geometry of a heptagon.
