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Proportions of bodies.
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Art or architectural creativity means use of proportional sizes for planning
art or architectural compositions as objects of compositions should have
harmonious positions in space of the art project.
Usually correct and beautiful ratio of objects in space calculate according to
proportions of golden section which is expression of harmony of world around.
The most obvious proportions of golden section are in ratio of lines in a
pentagon or in a dipentagon (ten-square figure), but also other geometrical
figures possess proportional and harmonious ratio of lines, and in particular
harmonious ratio exist in lines of a heptagon. Therefore for calculation of
proportional sizes it is possible to use lines of heptagonal or diheptagonal
geometrical network. Namely proportional sizes can be calculated by means of
measuring tools which are constructed according to lines of diheptagonal
geometrical network.
As a matter of fact lines of a heptagon possess special proportional ratio which
differ from proportions of golden section, but the gold section can be in lines
of a heptagon in the event that the heptagon is entered within the limits of an
alive circle.
The charts show multi-colored set-squares (the multi-colored elbow rulers) which
are constructed according to lines of the diheptagonal geometrical network and
are universal measuring tools.
Set-squares are constructed from the geometrical network of lines which is
entered within the correct circle, and the living circle is not
used as mathematical ratio of the living circle are very complex and in essence
are not required for decisions of simple art tasks.
Twenty shown set-squares are sufficient to construct any architectural
drawing or any art figure.
For example, by means of the first set-square it is possible to measure size of
human growth, and by means of the fourth set-square it is possible to measure
size of a head, as shown in the following chart:
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The geometrical network of lines is necessary for
scaling according to the sizes of the prospective art image or the
architectural plan, then it is necessary to isolate necessary
set-squares from the geometrical network of lines and then it is
possible to make measurements. Namely used set-squares should be derivatives from lines which are scaled according to the demanded sizes, and in particular the geometrical network of lines should be scaled according to the sizes of a human body if an art problem is the image of a woman. |
Construction of the figure of a human body is a complicated problem but by
means of the shown set-squares it is possible to calculate any fragments of a
body, and possible to determine position of fragments of a body in art space.
And also it is possible to isolate from lines of the diheptagonal network any
other figures which can be used as measuring tools. For example, it is possible
to take proportional or otherwise to tell "unequal set-squares" which are shown
in following chart:
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Proportional or unequal set-squares differ that unequal legs
(wings) have. Advantage of unequal set-squares consists that for calculation of proportional sizes it is possible to use any one unequal set-square when for calculation of the same sizes it is necessary to use two and sometimes three equal set-squares. And also unequal set-squares can be used for construction of prospects in art space. For example, the art task consists that is necessary to plant a tree in a garden. For this purpose it is possible to take any unequal set-square and to scale it concerning the sizes of a garden (plan-scheme of a garden), then it is possible to compare the ends (legs) of a set-square to any objects available in a garden and then to determine a place for planting a tree in the basis or in the top of set-square. Namely set-squares have the long leg X, the short leg Y, the top O and the basis Z, that is shown in the following chart. Hence, it is possible to connect the legs of a set-square with other trees in a garden and to put a new tree in point Z or in a point O and as a result positions of trees will correspond to proportions of lines in a heptagon. If in a garden there are some objects then by means of equal and unequal set-squares it is possible to coordinate a place of a planted tree with all objects existing in a garden. As a result planted tree will be harmoniously connected with objects of a garden as set-squares are derivatives from lines of the diheptagonal geometrical network in which proportional harmony of world around is included. |
Various set-squares and proportional set-squares can be considered as a set
of geometrical elements by means of which it is possible to make logic puzzles.
Planting of a tree in a garden, and also other architectural or art tasks can be
logic puzzles which decision is rather entertaining action if the problem is
solved by means of set-squares.
Besides lines of the diheptagonal geometrical network can consider as a
proportional compasses that is shown in following chart:
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The shown figure is a proportional compasses which
consists of two unequal set-squares which are connected in tops by means
of a hinge. Namely set-squares can move relative each other, and a point of relative movement are tops where there is a hinge or a meant hinge. The chart shows one proportional compasses which is an example, but similarly it is possible to isolate other necessary proportional compasses from lines of the diheptagonal geometrical network. |
Proportional compasses allow to measure and calculate sizes
which can be scaled during calculations.
Namely set-squares should be preliminary scaled according to the sizes of an
art project, and by means of proportional compasses it is possible to scale sizes during calculations.
For example, there is some magnitude XY for which it is necessary to determine
proportional magnitude X1Y1. For
this purpose it is necessary to correlate the legs of a proportional compasses
with magnitude XY and as a result we shall receive proportional magnitude X1Y1
which corresponds to distance between the adjacent legs of a proportional
compasses.
I can not result more examples for use of the shown measuring tools as any art
task consists in the unique decision of this task. There are no identical art tasks
and consequently each decision is the act of creativity as a result of which
every possible geometrical decisions can be found.
The set-squares and proportional compasses are
universal measuring tools which allow to solve various geometrical tasks.
Compasses and set-squares (elbow rulers) are sacral symbols which symbolize
sacred harmony and mean "tools of creation of the world". On some icons it is
possible to see images of set-squares which are combined with a figure of the
Christ and symbolize wings of cherubs that means harmony of the spiritual world,
and also a compasses with a set-square are an emblem of masons as are attributes
of builders or architects.
The following page results some geometrical puzzles which can be made of set-squares in the diheptagonal geometrical network.
