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Proportions of bodies.
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The heptagonal geometrical network of lines is a universal figure which
during development of the human civilization was used for measurement of
proportional ratio and for creation of objects in which
people aspired to fix principles of harmony.
Or it is possible to tell that people aspired to cipher knowledge of world
around in the created objects of human culture for what people used proportional
ratio of a heptagon which is the most significant figure expressing proportional
ratio comparable to proportions of a human body.
The most significant monument of human
knowledge are the Egyptian Pyramids (Great Pyramid of Giza), and in particular the Great Pyramid of Cheops
(Khufu) among many objects of the world.
I can not result the detailed analysis of all Egyptian Pyramids and
consequently I bring the description only for pyramid of Cheops as this pyramid
the most significant. But nevertheless the analysis of geometrical proportions
of other Egyptian Pyramids can be made in comparison with pyramid of Cheops.
The basic sizes of Cheops' pyramid are:
- length of the side basis is 500 cubits (elbows);
- height is 318
cubits;
- angle of incline of
lateral sides is 51 degrees 50 minutes.
The Egyptian cubit has size 466 millimeters that is approximately equal to
length from elbow up to the basis of fingers if growth of a man makes 176
centimeters.
In different sources of the information there are different data on size of
the Egyptian cubit, but 466 millimeters are taken from sources of the information which
is authentic from my point of view as it is anthropometrical size.
According to the listed sizes the main proportions of the Cheops' pyramid
consist in ratio of the triangle which is formed by height OP, half of length
of the basis PR and apothem (length of the lateral side) OR that
is shown on the chart:
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The number of the golden section
is ciphered in ratio of lines OR/PR (this is the famous Golden Ratio
solution or Gold Section, also known as the Divine Ratio), and
the number Pi is ciphered in ratio of lines PR/PO. Angle PRO with top in point R is the angle of incline of lateral sides, and angle PSO with top in point S is the angle of incline of diagonal edges. The angle of incline of lateral sides and the angle of incline of diagonal edges have different magnitudes in pyramid. Angle PRO and angle PSO are key parameters which allow to compare proportions of the Cheops' pyramid to proportions of a heptagon. |
Many researchers of the Pyramid of Cheops assume that the number of gold section and number Pi were known to builders of the Egyptian Pyramids, and also researchers assume that these gold numbers were key in the project of pyramids, but actually the knowledge of these numbers is not necessary as the knowledge of proportions of a heptagon suffices for construction of pyramids, and also it is enough to use ratio of lines which exist in a geometrical figure of a heptagon, that is shown in following chart:
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The triangle AEK is an approximate silhouette
of lateral sides of the Cheops' pyramid. The shown silhouette of lateral sides is approximate as the angle of heptagon AEK with top in the point K has size 360/7=51,429 degrees (51 degrees 25,71 minutes), and the angle of incline of lateral sides of the Cheops' pyramid has size 51 degree 50 minutes. Builders compensated the existing difference by addition of size of human growth AH to height of triangle AEK. Namely builders of the Cheops' pyramid have placed in top of a triangle and have conditionally placed a figure of a man at top of a pyramid and as a result have received corner EKX with top in the point K which have size 51 degrees 50 minutes. Namely if the height of triangle XEK is 318 cubits then height of triangle AEK is approximately 314 cubits provided that a height of human growth is 4 cubits. |
Builders of the Cheops' pyramid have increased the correct angle of a
heptagon as if at top of the pyramid there is a man, and as a result builders
have ciphered number of the golden section in ratio of lines EK/KX and have
ciphered proportions of a human body in proportions of the pyramid, that was a project of
the pyramid.
In essence builders of the Cheops' pyramid have entered the heptagonal network
of lines in a living circle in which the size of vertical diameter differed from
size of horizontal diameter in relative size of human growth that is shown in
the following chart:
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The diheptagonal network of lines is entered within a living circle which has a ratio of
vertical and horizontal diameters approximately 15/14 that corresponds
to ratio in proportions of a male and a female bodies. I can not tell more definitely about exact ratio of diameters of an alive circle in the geometrical drawing and in a project of the pyramid of Cheops as more exact calculations are necessary for this purpose. It is possible to assume that the ratio of diameters of a living circle in the geometrical drawing of the Cheops' pyramid turns out as a result of transformation of a living circle when size of the line TA is precisely equal to size of lines CE or DF. The dark blue contour in the chart specifies an approximate silhouette of lateral sides of the pyramid, and the white contour specifies an approximate silhouette of diagonal edges. Angle DLA with top in point L is the angle of incline of diagonal edges of the Cheops' pyramid which valid magnitude is 40 degrees 59 minutes. The magnitude of angle DLA and also the magnitude of angle EKA with top in the point K (the angle of incline of lateral sides) differ from angular magnitudes of a correct diheptagon in relative size of human growth according to which a living circle is transformed. |
The shown geometrical drawings are approximate as for exact geometrical
calculations many numbers and formulas are necessary, that is inexpedient in a
context of this gallery of phantom images, but according to the shown drawings it is
possible to do exact geometrical calculations if it is necessary.
The given drawings allow to understand the basic proportions of the
Egyptian Pyramids, but besides in geometrical measures of pyramids there are many other
the ciphered proportions according to which the world around
is arranged.
It is possible to speak that magnitudes of the Egyptian Pyramids have fixed
sizes of measurements which allow to understand structures of world around, and
allow to apply "Great Egyptian Measures" to designing environmental space and
for arrangements of the objects in the human world created by people.
The basic size of measurement in ancient Egypt is the cubit which consist of
seven palms, and each palm was subdivided into four fingers. Total the cubit
consist of 28 fingers that corresponds to 28 days of lunar month.
Pay attention that the diheptagonal network of lines has 14 tops, and the
quadraheptagonal network of lines has 28 tops that also is equal to number of
days in lunar month.
In a modern science about ancient Egypt there are different parameters of the
Egyptian cubit:
1 ordinary Egyptian cubit = 6 palms = 24 fingers = 450 millimeters;
1 royal Egyptian cubit = 7 palms = 28 fingers = 525 millimeters.
But however the size 466 millimeters is the most authentic as it is
anthropometrical size of a human elbow.
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The photo at the left shows the wooden panel where the land
surveyor with the measuring rod (measuring wand) in a hand is
represented, namely the photo shows one of 11 wooden carved panels which
were found in the tomb of Hesi-Ra who is considered as the architect
of Egyptian Pyramids. The found panels have images on both sides that in the sum is comparable to 22 arcane of cards Tarot. There is hypothesis that the found 11 wooden panels became a reason of the esoteric legend that predictive cards of Tarot have the Egyptian origin. The measuring rod in a hand of the land surveyor is equal to length from middle of a body up to a line of eyebrows that makes two cubits. If to project this measuring rod on the diheptagonal network of lines then the rod is equal to line AT, and also it is approximately equal to length of the side of a heptagon that is shown in the previous chart. Namely the measuring rod is equal to lines CE, DF, LJ, MK. Hence, the Egyptian cubit is equal to length of the side of a diheptagon (to distance between two near tops), and any other sizes of measurements are derivatives from the diheptagonal geometrical network in which the figure of a human body is entered that allows to do the statement about ratio of the Egyptian Pyramids with proportions of a human body. But provided that the diheptagonal network is entered in a living circle which forms "an ellipse with a focal length proportional to human growth taken in the attitude to height of the pyramid". Otherwise it is possible to tell that the difference of diameters (difference of the big and small axes of an ellipse) corresponds to the attitude of human growth to height of the Pyramid. |
Builders have calculated the sides of pyramids by means of the measuring rod,
and in a project of the Khafre's Pyramid (The Pyramid of Chephren) there was
"sacred Egyptian triangle" with the attitude of the sides 3:4:5 that has other
name "sacred Pythagorean triangle", and in a project of the Cheops' pyramid
there were proportions of a human body. Namely the Pyramid of Chephren and the
pyramid of Cheops have the different sizes but both pyramids are calculated
according to one measuring rod. Apparently different pyramids have been
calculated as a result of different transformations of lines in the diheptagonal
geometrical network.
The additional information on the sacred Egyptian or Pythagorean triangle
with the attitude of the sides 3:4:5 look on pages of other website:
www.emotions.64g.ru/prof3/pro04en.htm
The following page in detail tells about measuring tools which can be derivatives from lines of the heptagonal geometrical network.
