geometry of heptagon and ideal proportions

measures of a human body

Page 1.

gymnastic exercises and training
principle of global harmony
mathematical patterns of proportion
linear networks of heptagonal figures
bodies of people and geometrical ideals
sizes and measurements
shaping clubs and bodybuilding
physical culture of a body

shaping and bodybuilding or aerobics and rhythmic gymnastics  

Linear networks and geometrical figures of somatic shapes.
The first page shows ideal proportions of a human body according to geometrical lines of heptagon.

Concepts of ideal proportions can be interesting in view of shaping and bodybuilding, and also aerobics and rhythmic gymnastics, as correct shapes of human bodies are the purpose of sports exercises and training, and also physical culture of a body.


Ideal geometrical proportions of somatic shapes.
Figure of heptagon and pattern models of a body.

Principles of global harmony or otherwise to tell harmonious proportions of the world validity are caused by geometrical figures of correct polygons.
One of figures is the heptagon and linear geometrical network which exists as a result of connection of tops in heptagon by lines. This heptagonal network of lines can be considered as the most significant spatial figure among other correct polygons as it corresponds to proportions of a human body, that is shown on the scheme.
The additional information on heptagonal geometrical network of lines look in other section of this website in concepts of the Japanese garden of stones where proportions of heptagon are compared to rules of stone arrangements.


ideal somatic shapes of female figure in lines of heptagonal network The grey contour shows the ideal somatic shapes of human figure which is entered in lines of heptagonal network.
The shown figure of a body is female, and proportions of ideal male somatic shapes see below.
Height or stature of a human body shares on 8 parts according to the ancient Greek sculptural canon, and the head size has 1/8 part from a stature height, that is shown on the scheme by blue lines.
Actually sizes of human heads have 1/8 part if statures are180 centimeters, but if statures are 175 or 170 centimeters then sizes of heads have approximately 1/7,5 or 1/7 parts according to average anthropometrical measurements. Namely human heads are proportional to vertical sizes of bodies. But however sizes of a head in the fine arts are considered as ideal if somatic proportions correspond to the Greek sculptural canon.
It is necessary to tell that the ancient Greek canon of proportions of human bodies was not kept, namely libraries have only particles of the text, but in essence the content of Greek sculptural canon is not known. Namely historians and artists consider that the canonical head has 1/8 part of stature, as it is possible to measure such proportions in the Greek sculptures, but actually any descriptions of sculptural parameters and concrete texts are absent.

The shown grey contour can be used in the fine arts as basic geometrical model or the pattern stencil which allows to draw ideal proportions of a female body. As this pattern designates lines of the thigh (hips) and trunk (shoulders), that corresponds to the basic geometrical parameters and somatic shapes which are sufficient for formal measurements and drawing of ideal female body.
But to measure parameters of other lines of a body it is necessary to use more complex pattern which is constructed in lines of geometrical figure with fourteen angles or otherwise to tell in diheptagonal linear network. Or it is necessary to use patterns in linear crossings of triheptagonal or quadraheptagonal networks which are even more complex, but which allow to measure contours of hands and legs, and also other somatic shapes for not only female, but also male bodies. That is possible to see on following scheme where pattern stencils of ideal female and male bodies are included in space of the diheptagonal linear network. And also it is possible to see on pages of this website in galleries where some graphic drawings and art pictures represent figures of human bodies which are constructed according to lines of triheptagonal and quadraheptagonal geometrical networks.

somatic shapes of human bodies and proportions of the Greek sculptural canon Shapes of female body correspond to the grey contour, and the pattern of ideal male figure is shown by green color
Diheptagonal linear network allows to measure more geometrical points of a human body rather than lines of heptagon, and if to use triheptagonal or quadraheptagonal networks then proportional shapes of human bodies can be measured very in detail.


If to look at the figure of female body it is possible to see that crossing of lines EJ and FK corresponds to knees, and crossing of lines AH and DL corresponds to the umbilicus. Also it is possible to find geometrical points of a human body in crossings of other lines.
The male figure is generated by crossings of other lines rather than shapes of a female body, but both pattern stencils correspond with lines of diheptagonal network. Therefore the heptagon is a basic geometrical figure which correspond with somatic shapes of human bodies and proportions of the Greek sculptures.
It is necessary to consider that proportions of male and female bodies according to statistical anthropometrical data have ratio 15/14 (exact geometrical data 528/472). Namely if stature of a man has size of 150 centimeters then height of a woman is 140 centimeters. Or if average statures of men are 176 centimeters then average heights of women are 164 centimeters, that corresponds to general anthropometrical measurements.
Therefore for use in the fine arts it is necessary to transform geometrical figure of the diheptagonal linear network that pattern stencils of human bodies can have valid proportions, that is shown in following scheme.

pattern stencils of human bodies in the linear network of alive circle The diheptagonal linear network of this scheme is transformed within the limits of "alive circle" in which ratio of vertical and horizontal diameters approximately is 15/14, that corresponds to proportional parity of male and female body shapes.
In essence this scheme shows the ellipse or oval in which the long axis corresponds to male body proportions, and the short axis corresponds to proportions of female body shapes.
Shown positions of somatic figures in the diheptagonal network have angular ratio 360/14=25,714x3=77,143 degrees that deforms proportions of female pattern. But if to use the quadraheptagonal network of lines then figures of male and female patterns of somatic shapes can be located with angular ratio of 90 degrees, and then proportions of patterns will not be deformed and can be used in the fine arts.
The shown ellipse can be named as "alive circle" because such term is used in geometry for definition of the alive square with ratio 15/14 in attitudes of sides.

The shown geometrical patterns of somatic shapes are approximate, but can be used for drawing of human bodies or for measurements in anthropology, that is enough for the fine arts and formal anthropological measuring. Or the shown patterns or otherwise to tell geometrical models of ideal male and female bodies can be applied to exact calculations in mathematics, that can be necessary in various spheres of a human life. In particular in the fashion industry for design of clothes, or in show business for objective estimations of appearance at competitions of models and beauty contests of female bodies.
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 this online art gallery of phantom images, but exact calculations can be executed according to the submitted geometrical concepts.
Additional information on sizes of somatic shapes and proportions of human bodies for exact calculations look in other data sources.
I should tell that the presented concepts about ideal proportions of a human body on pages of this website are before not known, but I approve that ratio of human geometrical shapes with figures of correct polygons correspond to principles of global harmony, that can be a theme for the further researches.

The following page considers proportions of the Egyptian Pyramids in view of geometrical forms of heptagon and somatic parameters of a human body.

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