THE CASING STONES
A few of the fine limestone casing blocks remain at the base of the northern
side and show how accurately the stones were dressed and fitted together.
The core masonry, behind the casing stones, consists of large blocks of
local limestone, quarried right on the spot, built around and over the
bedrock core. The size of this core cannot be determined, since it is
completely covered by the pyramid.
The casing stones were of highly polished white limestone, which must have
been a dazzling sight. Unlike marble, which tends to become eroded with time
and weather, limestone becomes harder and more polished.
HOW MANY BLOCKS DID IT ACTUALLY TAKE TO BUILD
THE GREAT PYRAMID?
Most books and encyclopedia state that there are 2.3 million blocks of stone
in the Great Pyramid of Khufu (Cheops), with no mention of method used to
Socrates determined the size and weight of the blocks (a standard block),
and ran a Pascal Computer Program (a mathematical model of all the blocks of
stone needed; written by the author to optimize the sizes and weights of the
stones) to come up with the real number of blocks used. Since the volume of
passageways and internal chambers are very small compared to the high volume
of the pyramid, they are ignored at this time, just as though the pyramid
was built of solid stone blocks with mortared joints.
THE SIZE OF THE BLOCKS
The size of the blocks are based on a chance discovery in 1837 by Howard
Vyse. He found two of the original side casing blocks at the base of the
pyramid, 5 ft x 8 ft x 12 ft, with an angle of 51 degrees, 51 minutes cut on
one of the 12 ft. sides. Each of these stones weighed (5 x 8 x 12)/2000 =
39.9 tons before the face angle was cut. These originally were used for the
side casing stones of Step No. 1, in the Pascal computer program. The sizes
of all the other blocks were scaled from these two original blocks of the
remaining Steps 2 to 201.
THE GREAT PYRAMID'S DIMENSIONS AND THEIR LAYOUT
One acre = 43,560 sq. ft, or 208.71 feet on a side.
For the pyramid's base, length = width = (square root of 13.097144 acres) x
208.71 feet = 755.321 feet. Or 755.321 x 12 = 9063.85 inches.
Height = (755.321 x tangent 51deg 51 min)/2 = 480.783 feet. Or 480.783 x 12
= 5769.403 inches.
For the cap stone base: length = width = (32.18 x 2)/tangent 51deg 51 min =
The average size of a pyramid stone = (5 x 8 x 12)
The average side measurement, at the base = 759.3 ft.
The height used was 201 steps high, or 480 feet. (This is minus the height
of the Capstone, which was one piece in itself.
The number reached by the Pascal computer program was 603,728 blocks used.
The solid core takes up the space of 13,016 stones.
So, the actual number of stones used to build the Great Pyramid is 603,728 -
13,016 = 590,712.
This figure is (2,300,000 - 590,712) = 1,709,288 blocks less than the often
published 2.3 million value.
NUMBER OF VARIOUS BLOCKS OF STONE USED
TO BUILD THE GREAT PYRAMID
Number of platform blocks used (2.5 ft x 10 ft square), equals (759.3 x
759.3(pyramid base)) - (412.7 x 412.7(core base))/(10 x 10(platform block
base)) = 4,062.
Number of CORNER Casing stones where the pyramid faces meet equals 201 steps
x 4 sides = 804.
Number of side casing stones equals ((244 x 127) + 8,953) = 39,941.
Due to Bedrock Core, in the center of Step 1 through 10, the total number of
blocks needed is reduced by 13,016.
THE NUMBER OF ALL BLOCKS BEHIND
THE CASING STONES EQUALS
(590,712 - 804 - 39,941) = 549,967.
PLACING THE BLOCKS
The average number of blocks that have to be placed each day equals (590,712
blocks)/(20years x 364.25 days) = 81 blocks per day.
If 10 crews of 300 men work on each of the four sides of the pyramid, then
the totals of 40 crews and 12,000 men will be needed. Each of the crews will
be responsible to place 81/40 = 2 blocks per day.
The workload passes through three phases of decreasing difficulty, which are
determined by the weights of the heaviest blocks:
Steps 1 through 21 (60.59 to 27.24 tons)
Steps 22 through 136 (17.66 to 6.44 tons)
Steps 127 through 201 (3.05 to 2.63 tons)
As the weight of the blocks decrease, Step to Step, the sizes of the drag
crews will decrease. However, when this happens, the number of blocks needed
to be dragged each day can be reduced because one large block can be dragged
and cut into several smaller blocks that are needed.
As the pyramid rises there is less space for the crews to work in and fewer
block to be placed. In other words, the number of workers that will be
needed depends on three factors of: weight of blocks, number of blocks to be
placed, and the working space available.
Back in Time 3104 B.C. to the Great Pyramid- Egyptians Broke Their Backs to Build It- How the Great Pyramid Was Really Built
© 1990 by Socrates Taseos
Related Books on the Ancient Egypt
Geometry of the Great Pyramid
DIMENSIONS of Great Pyramid
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If the calculations concerning the royal cubit are correct the main dimensions of the pyramid should also prove that. The approximate dimensions of the pyramid are calculated by Petrie according to the remains of the sockets in the ground for the casing stones whose remains are still at the top of the pyramid, and the angle 51° 52' ± 2' of the slopes. The base of 9069 inches is approximately 440 royal cubits (the difference is 9 inches which is not a remarkable difference if we consider the whole dimension and consider that the employed data represent only an estimation of the real values) whereas the calculated height, 5776 inches, is precisely 280 royal cubits. The relation 440:280 can be reduced to 11:7, which gives an approximation of the half value of Pi.
Squaring the Circle
The circle and the square are
united through the circumference:
area of square: 440x440=193600
area of circle:28x28x22/7=246400
The engagement of Pi value in the main dimensions suggests also a very accurate angle of 51° 52' ± 2' of the slopes which expresses the value of Pi. Another coincidence is the relation between the height of the pyramid's triangle in relation to a half of the side of the pyramid, since it appears to be the Golden Section, or the specific ratio ruling this set of proportions, F = (sqr(5)+1)/2 = 1.618 = 356:220. This ratio, 356:220 = 89:55 is also contained in the first of Fibonacci Series:
1 2 3 5 8 13 21 34 55 89 144 ...
A single composition contains two apparently contradicting irrational numbers P and F, without disrupting each other. This appears to be completely opposed to the classical architectural canon which postulates that in 'good' composition no two different geometrical systems of proportions may be mixed in order to maintain the purity of design.
But analysis of other architectural and artistic forms suggested that the greatest masters skillfully juggled the proportional canons without losing the coherent system, for they knew that these systems can be interconnected if the path that links them is found. That is obvious In the case of the Great Pyramid where two different principles are interweaved without interference ruling different angles of the composition, which is most importantly a most simple one, namely 11:7, a most simple ratio obviously signifying such infinite mysteries as the value of P and most 'natural' value of F. In spite of common miss-understanding of architectural composition, the most mysterious and praised compositions are very simple but not devoid of anthropomorphic appeal, since everything is made out of human proportions, just like Vitruvius describing the rations of the human body, very simple and very clean. The numbers 7 and in 11 are successive factors in the second of Fibonacci progressions that approximate geometry of the pentagram:
1 3 4 7 11 18 29 47 76 123 ...
The summary of the selected main mean dimensions is:
The main source of all kinds of delusions and speculations about our mythical past for the western man comes of course from Plato. With the myth of Atlantis he planted the necessary seed of mythical Eden, a culture of high intelligence that lived before the known history. If Plato received any wisdom from the ancient Egypt it could perhaps be traced in the canon of numbers that is so latently present throughout his work, but never on the surface. This canon seems to appear in the descriptions of his fantastic cities where everything is most carefully calculated and proportioned. The topic of Plato's Laws is the description of the ideal state called Magnesia which is entirely composed out of the mysterious number 5,040.
The distance* when Earth is closest to Sun (perihelion) is 147x106 km, which is translated into royal cubits 280x109, hinting at the height of the Great pyramid,
280 royal cubits.
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* Related links: Astronomic & Cosmographic Data, Nasa site with planetary data
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Find out more amazing facts about the GREAT PYRAMID: Position of King's Chamber, Queen's Chamber, Subterranean Chamber; SECOND PYRAMID: Dimensions of Pyramid, Great Chamber, Coffer, Lower Chamber; THIRD PYRAMID: Dimensions of Pyramid, Chambers,MATHESIS of Giza Plateau.
The Golden Ratio & Squaring the Circle in the Great Pyramid
A straight line is said to have been cut in extreme and mean ratio when,
as the whole line is to the greater segment, so is the greater to the less. [Euclid]
The extreme and mean ratio is also known as the golden ratio.
If the smaller part = 1, and larger part = G, the golden ratio requires that
G is equal approximately 1.6180
Does the Great Pyramid contain the Golden Ratio?
Assuming that the height of the GP = 146.515 m, and base = 230.363 m, and using simple math
we find that half of the base is 115.182 m and the "slant height" is 186.369 m
Dividing the "slant height" (186.369m) by "half base" (115.182m) gives = 1.6180, which is practically equal to the golden ration!
The earth/moon relationship is the only one in our solar system that contains this unique golden section ratio that "squares the circle". Along with this is the phenomenon that the moon and the sun appear to be the same size, most clearly noticed during an eclipse. This too is true only from earth's vantage point…No other planet/moon relationship in our solar system can make this claim.
Although the problem of squaring the circle was proven mathematically impossible in the 19th century (as pi, being irrational, cannot be exactly measured), the Earth, the moon, and the Great Pyramid, are all coming about as close as you can get to the solution!
If the base of the Great Pyramid is equated with the diameter of the earth, then the radius of the moon can be generated by subtracting the radius of the earth from the height of the pyramid (see the picture below).
Click here to view larger picture.
Also the square (in orange), with the side equal to the radius of the Earth, and the circle (in blue),
with radius equal to the radius of the Earth plus the radius of the moon, are very nearly equal in perimeters:
Orange Square Perimeter = 2+2+2+2=8
Blue Circle Circumference = 2*pi*1.273=8
Earth, Radius, Mean = 6,370,973.27862 m *
Moon, Radius, Mean = 1,738,000 m.*
Moon Radius divided by Earth Radius = 0.2728 *
* Source: Astronomic and Cosmographic Data
Let's re-phrase the above arguments **
In the diagram above, the big triangle is the same proportion and angle of the Great Pyramid, with its base angles at 51 degrees 51 minutes. If you bisect this triangle and assign a value of 1 to each base, then the hypotenuse (the side opposite the right angle) equals phi (1.618..) and the perpendicular side equals the square root of phi. And that’s not all. A circle is drawn with it’s centre and diameter the same as the base of the large triangle. This represents the circumference of the earth. A square is then drawn to touch the outside of the earth circle. A second circle is then drawn around the first one, with its circumference equal to the perimeter of the square. (The squaring of the circle.) This new circle will actually pass exactly through the apex of the pyramid. And now the “wow”: A circle drawn with its centre at the apex of the pyramid and its radius just long enough to touch the earth circle, will have the circumference of the moon! Neat, huh! And the small triangle formed by the moon and the earth square will be a perfect 345 triangle (which doesn’t seem to mean much.)
** Source: http://geometry.wholesomebalance.com/Sacred_Geometry_2.html#Phi
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