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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. (Additional information on
the heptagonal geometrical network of lines look in concepts of the Japanese
garden of rocks where proportions of the heptagon are compared to rules of an
arrangement of rocks.)
Including the heptagonal network 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). According to the Greek sculptural canon growth of a human body shares on 8 parts and the size of a head makes 1/8 part from growth of a body that is shown in the chart by dark blue lines. Actually, according to the average anthropometrical sizes, a head makes 1/7,5 from growth of a body, but nevertheless 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 of proportions of a human body was not kept, namely only a few phrases were kept but in essence the contents of a canon is not known. |
The shown figure can be used as a pattern which allows to draw ideal
proportions of a human body. Namely this pattern allows to measure lines of hips, waists and shoulders which are
the basic lines and consequently the shown pattern is elementary model of a body
which can be used for measurement of key parameters.
To measure detailed parameters of other proportional lines of a body, it is
necessary to use more complex patterns which are constructed in lines of the
diheptagonal network (fourteen-polygonal network), or it is necessary to use
lines of the triheptagonal network or the quadraheptagonal network which are
more complex.
The diheptagonal network allows to describe not only the ideal pattern of a
female body, but also the ideal pattern of a male body that is shown in the
following chart:
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In the chart the female figure is shown by grey
contours, and the male figure is shown by green contours. Within the framework of the diheptagonal network, be relative each other, figures of a male and female body are located at an angle of 360 / 14 = 25,714 õ 3 = 77,143 degrees that is approximately equal to the angle of top of the Great Pyramid of Cheops (the information on proportions of the Great Pyramid of Cheops look on following pages of this section of the site). The diheptagonal network allows to describe the greater number of proportional points of a human body, than it allows the heptagonal network, 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 other lines it is
possible to find proportional points of a human body.
Proportions of a male body are similar to proportions of a female body, but the
male figure within the framework of the diheptagonal network is generated from
crossing other lines, rather than the figure of a female body.
According to statistical anthropometrical measurements, proportions of a male
and female body have the parity 15 : 14 (the exact geometrical data 528 : 472).
Namely if average growth of the man makes 150 centimeters, average growth of the
woman makes140 centimeters. Or if average growth of the man makes 176
centimeters, average growth of the woman makes 164 centimeters that corresponds
to average anthropometrical measurements.
As proportional parities of a male and female body unequal, it is necessary to
transform the geometrical networks of lines shown in the charts that the figures
of human bodies entered in lines became appropriate to the valid proportions
that is shown in the following chart:
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In this chart the diheptagonal network of lines is
entered in frameworks of "living circle" in which the parity of vertical
and horizontal diameters approximately 15 : 14, that is coordinated with
proportional parities of a male and female body. In essence this chart shows an 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 framework of diheptagonal network has the parity of 77,143 degrees. Therefore to transform proportions of a male or female body it is necessary independently. If to use the quadraheptagonal network of lines then patterns of a male and female body can be located at an angle of 90 degrees and then figures of a male and female body can be transformed interconnected. The shown ellipse can be named: "living circle" as such term is used in geometry for a designation of the square (the living square) with the attitude of the sides 15 : 14. |
The given geometrical concepts of human bodies are approximate, but can be
used for exact calculations. If exact calculations of the sizes and proportions
are not actual, it is possible to use approximate patterns of a male and female
body 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 which
are required for exact calculations, look in other sources of the information.
Should tell, that the submitted geometrical concepts and theories differ from
known concepts, but I assert that the submitted geometrical concepts and
researches do not contradict principles of the global proportion and harmony.
The following page considers proportions of the Egyptian Pyramids which correspond with proportions of a human body and proportions of a heptagon.
