The Great Pyramid at the Giza Plateau, Egypt, is mysterious, mystical and strategically placed on the face of the Earth. It is aligned with the four cardinal points more accurately than any other  structure, even the Greenwich observatory. The builders displayed enlightened understanding of engineering, mathematics, physics and astronomy. They also had a profound knowledge of the Earth's dimensions. Many scientist and scholars now think it was built earlier than the reign of Cheops (Khufu) at 2600 B.C. They disagree with the traditional view of Egyptologist and attribute it to an advanced civilization before the rule of the Pharaohs. I am convinced they are right. For more details follow the "Egypt/Center of Earth" link.
The Pyramid lies in the center of gravity of the continents. It also lies in the exact center of all the land area of the world, dividing the earth's land mass into approximately equal quarters. It lies in the middle of Egypt and in the middle of Lower and Upper Egypt.
    
The Plate XX from an original 1877 copy of  Piazzi Smyth's "Our Inheritance in the Great Pyramid". Charles Piazzi Smyth (1819-1900) was Astronomer Royal for Scotland and a respected Scientist. 

The north-south axis (31 degrees east of Greenwich) is the longest land meridian, and the east-west axis (30 degrees north) is the longest land parallel on the globe. There is obviously only one place that these longest land-lines of the terrestrial earth can cross, and it is at the Great Pyramid! This is incredible, one of the scores of features of this mighty structure which begs for a better explanation.

Pyramid Statistics  © 2000 by Larry Orcutt,A total of over 2,300,000  blocks of limestone and granite were used in its construction with the average block weighing 2.5 tons and none weighing less than 2 tons. The large blocks used in the ceiling of the King's Chamber weigh as much as 9 tons. 

Original entrance of the Great Pyramid. Massive blocks of limestone form a relieving arch over the entrance. 

• The base of the pyramid covers 13 acres, 568,500 square feet and the length of each side was originally 754 feet, but is now 745 feet. 
• The original height was 481 feet tall, but is now only 449 feet.

The majority of the outer casing, which was polished limestone, was removed about 600 years ago to help build cities and mosques which created a rough, worn, and step-like appearance. The base measurements of the Great Pyramid are: north - 755.43 ft; south - 756.08 ft; east - 755.88 ft; west - 755.77 ft. These dimensions show no two sides are identical; however, the distance between the longest and shortest side is only 7.8 inches. Each side is oriented almost exactly with the four Cardinal points. The following being the estimated errors: north side 2'28" south of west; south side 1'57" south of west; east side 5'30" west of north; and west side 2'30" west of north. The four corners were almost perfect right angles: north-east 90degrees 3' 2"; north-west 89 degrees 59'58"; south-east 89 deg 56'27"; and south-west
90 deg 0'33". When completed, it rose to a height of 481.4 ft., the top 31 feet of which
are now missing. It's four sides incline at an angle of about 51deg. 51 min. with the ground. At its base, it covers an area of about 13.1 acres. It was built in 201 stepped tiers, which are visible because the casing stones have been removed. It rises to the height of a modern 40-story building.

THE BEDROCK AND CORE

The pyramid is built partly upon a solid, large, bedrock core and a platform of limestone blocks which can be seen at the northern and eastern sides. The builder of this pyramid was very wise to choose this site because most of the stones, with the exception of the  casing stones, some granite and basalt stones, could be cut right on the spot and in the nearby quarry. This practical choice made it possible to reduce considerably the time and back-breaking labor needed to drag the stones from distant quarries across the Nile.

The many surveys done on the pyramid proved that the Egyptians located the sides of the pyramid along the four Cardinal Points with extreme accuracy. Whether they used the stars, and/or the rising and setting sun, cannot be determined. One this is certain, that whatever method they used was direct and very simple.

Once the sand, gravel and loose rocks had been removed, down to the solid bedrock of the plateau, the whole pyramid site was open-cast quarried into blocks, leaving a square core for the center of the pyramid (the core is approximately 412.7 ft square, and rises approx. 46.25 feet high). These blocks were then stored outside a low wall; made of mortared stone that surrounds the core (the outside dimensions of the wall are approx. 887.3 feet square). Today there still remains the foundation of this wall on the north, south and west sides of the pyramid, at an average distance of 65 feet from the outer edge of the base casing stone.

This core gives the pyramid stability from the downward and horizontal forces that will develop from the superimposed loads of blocks of stones that are piled up, as the pyramid rises. Also, from the prevailing north-west winds that exert enormous pressures on the huge areas of the pyramid's faces, thus increasing these forces further.

Leveling of the entire pyramid site was accomplished by flooding the area inside the wall with water, leaving just the high spots. These them were cut down to the level of the surface of the water. Next, some of the water was released and the high spots again were cut down to the water's surface. This
process was repeated until the entire pyramid site, between the core and the four walls, was leveled down to the base of the pyramid's platform.

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.

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 =
50.55 inches.

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. Geometry of the Great Pyramid 

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. 

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).

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

Note: 
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.)

Was the golden ratio intentionally built into the Great Pyramid of Cheops? 
Why would anyone intentionally build the golden ratio into a pyramid, or other structure? What was the significance of to the Egyptians? And did the ancient Egyptians intentionally design the Great Pyramid to square the circle?

The answer to these questions is uncertain since designing the Great Pyramid according to the simple rules explained by the graphic below would give the pyramid automatically (by coincidence? ) all its "magic" qualities. 

The height of the Great Pyramid times 2π exactly equals the perimeter of the pyramid. This proportions result from elegant design of the pyramid with the height equal two diameters of a circle and the base equal to the circumference of the circle.  Click here or on the image below to see larger picture.

For the angle of the Great Pyramid, any theory of the base, combined with any theory of the height, yields a theoretic angle; but the angles actually proposed are the following** :

** Page 184, The Pyramids and Temples of Gizeh 
     by Sir W.M.Flinders Petrie 1883

Comparing the Great Pyramid with the Pyramid of the Sun in Teotihuacan

The Pyramid of the Sun and the Great Pyramid of Egypt are almost or very nearly equal to one another in base perimeter. The Pyramid of the Sun is "almost" half the height of the Great Pyramid. There is a slight difference. The Great Pyramid is 1.03 - times larger than the base of the Pyramid of the Sun. Conversely, the base of the Pyramid of the Sun is 97% of the Great Pyramid's base.

The ratio of the base perimeter to the height:

The Great Pyramid - Metrological Standard

The Great Pyramid is generally regarded as a tomb and as grandiose memorial to the pharaoh who commissioned it.  The opposing view is that of the pyramid being the culminating achievement of those who practiced an advanced science in prehistory.

The Great Pyramid is a repository of universal standards, it is a model of the earth against which any standard could be confirmed and corrected if necessary. 
It is exactly the imperishable standard, which the French had sought to create by the devising of the metre, but infinitely more practical and intelligent. 

From classical times, the Great pyramid has always been acknowledged as having mathematical, metrological and geodetic functions. But ancient Greek and Roman writers were further removed in time from the designers of the Great Pyramid than they are from us. They had merely inherited fragments of a much older cosmology; the science in which it was founded having long since disappeared.

The Concave Faces of the Great Pyramid 

Aerial photo by Groves, 1940 (detail).

In his book The Egyptian Pyramids: A Comprehensive, Illustrated Reference, J.P. Lepre wrote:

One very unusual feature of the Great Pyramid is a concavity of the core that makes the monument an eight-sided figure, rather than four-sided like every other Egyptian pyramid. That is to say, that its four sides are hollowed in or indented along their central lines, from base to peak. This concavity divides each of the apparent four sides in half, creating a very special and unusual eight-sided pyramid; and it is executed to such an extraordinary degree of precision as to enter the realm of the uncanny. For, viewed from any ground position or distance, this concavity is quite invisible to the naked eye. The hollowing-in can be noticed only from the air, and only at certain times of the day. This explains why virtually every available photograph of the Great Pyramid does not show the hollowing-in phenomenon, and why the concavity was never discovered until the age of aviation. It was discovered quite by accident in 1940, when a British Air Force pilot, P. Groves, was flying over the pyramid. He happened to notice the concavity and captured it in the now-famous photograph. [p. 65]

This strange feature was not first observed in 1940. It was illustrated in La Description de l'Egypte in the late 1700's (Volume V, pl. 8). Flinders Petrie noticed a hollowing in the core masonry in the center of each face and wrote that he "continually observed that the courses of the core had dips of as much as ½° to 1°" (The Pyramids and Temples of Gizeh, 1883, p. 421). Though it is apparently more easily observed from the air, the concavity is measurable and is visible from the ground under favorable lighting conditions.

Ikonos satellite image of the Great Pyramid.
Click to view larger image.

I.E.S. Edwards wrote, "In the Great Pyramid the packing-blocks were laid in such a way that they sloped slightly inwards towards the centre of each course, with a result that a noticeable depression runs down the middle of each face -- a peculiarity shared, as far as is known, by no other pyramid" (The Pyramids of Egypt, 1975, p. 207). Maragioglio and Rinaldi described a similar concavity on the pyramid of Menkaure, the third pyramid at Giza. Miroslav Verner wrote that the faces of the Red Pyramid at Dahshur are also "slightly concave."

Diagram of the concavity (not to scale).

What was the purpose for concave Grea the first pyramid should hold true for the others."

Three proposed "baselines" of the Great Pyramid (not to scale).

The purpose for the concavity of the Great Pyramids remains a mystery and no satisfactory explanation for this feature has been offered. The indentation is so slight that any practical function is difficult to imagine.

© 2000 by Larry Orcutt,  Catchpenny Mysteries, Reprinted with permission

The Great Pyramid's "Air Shafts"

Shafts and passages of the Great Pyramid at Giza.

http://genesis.allenaustin.net/pyramid.htm

JOSEPH TURBEVILLE'S RESEARCH

A Glimmer

Of Light

From the Eye

Tabular evidence of a monument in harmony with the universe

 

NOTE:   This book by a former Physics Professor contains one of the most fascinating mathematical analysis of the Great Pyramid that I have ever read.  It is loaded with charts and tables and Professor Turbeville displays a grasp of mathematics that is unique.  His correlations are very creative and insightful.    I highly recommend this book and I guarantee you will find it challenging, stimulating, and enjoyable.

John DeSalvo, Ph.D., Director
Great Pyramid of Giza Research Association

 

Preface

If anyone should ask how I managed to conceive the idea and why I decided to develop the tables presented in this treatise, I’m not certain I‘ll be able to give them a reasonable and acceptable answer. This is an attempt.

I’ve always considered myself a creative and intuitive person who enjoys the symmetry and beauty of the world around me. A trip to a boatyard or marina to gaze at the sleek hulls of sailing vessels gives me quiet pleasure. The solution to a difficult math problem may sometimes come to me in an intuitive flash and always seems beautiful. In the last few years I have become increasingly aware of what are called synchronistic events in my life, where coincidental happenings no longer seem merely coincidental but often have real personal meaning or affect the activity I may be involved in. It was in this light that I found myself creating, or quite possibly recreating, these extremely interesting tables that seemed to come to me from out of antiquity and have provided me with a real sense of discovery. Number summations and symmetrical combinations discovered in the tables amazingly represent many of the exact measurements made at the Great Pyramid in Egypt. Other numbers that continually reoccur in the tables represent physical earth measurements of such things as size, density, angular velocity and rotational energy, or harmonics thereof. It seems impossible to imagine that all of these factual numbers were placed here by mere coincidence, when a knowledge of higher mathematics seems essential for their presence, so many so that the reader may be tempted to join in the search for other numerical connections to the distant past. This is my hope and indeed may be the reason for this revelation.

 

I did not intend this to be a treatise on the synchronistic events that may have led me to this fascinating discovery and these events will only be discussed or mentioned as side notes at those points in this work where I feel it necessary for the reader to be shown how I might have been given a nudge in a fruitful direction by some synchronistic event. This is done in order to minimize any aura of mysticism that might be cast over these tables, for truly they are nothing more than an additive sequence of numbers and combinations thereof that may be found in all of nature.

 

The Great Pyramid - Khufu

The mystery that surrounds the Great Pyramid of Giza in Egypt is legendary, and the differences between truth and legend become less certain as we travel back through the mist of time. It is the most studied and written about monument on the face of the Earth, and it is not my intention to add more verbiage to the vast collection of literature already available on the subject.

It is my intention, however, to show that the tables developed and presented here were inspired by the mathematical symmetry found in nature and for some mysterious reason contain the most precise measurements ever made of the major dimensions of the Great Pyramid Khufu. Only after I began to probe the symmetry and mirror image properties of the tables did I begin to wonder; "Might similar tables have existed before the Great Pyramid was built? Do they contain data or guidelines that might have been used by ancient artisans and architects?"

Using the precise width and height measurements recorded by William Petrie, an English surveyor of the late nineteenth century as a reference, ¹ 440 royal cubits for the base width, 280 royal cubits for the height, and in addition, using his determination of the royal cubit of 20.63 inches, which is now an accepted standard for the Great Pyramid, a base width of 756.4 feet and height of 481.4 feet can be calculated.

There seems to be no direct evidence in the tables of any number that is sufficiently close to the height in feet shown above to be acceptable; however, there are an excess of dimensional numbers from which the height can be calculated. These external numbers can be physically measured on the pyramid, whereas the height is a number that must be calculated. There is no way to make a direct internal measurement of the height. The base line width 756 feet, the half width 378 feet, the apothem length 612 feet (a measure from the apex down the pyramid face to the half-width point) and the corner edge line 720 feet can all be found in the tables.*

If the total sum of the numbers of Table-1 (1188) is divided by 189, an ancient irrational value once used for two Pi (2p ) is obtained. i.e. 1188 / 189 = 44/7 = 2p .

This irrational value of Pi (p ) = 22/7 is in error by only 0.04 % and is used throughout this entire treatise as it seems to be the value in use when the pyramid was built.

In the earlier discussion on Khufu – A Model of the Earth, we discussed the fact that 360° had historically been known to contain 21600 arc minutes and that a minute of arc on the Earth’s surface was equal to one nautical mile. If we assume that the total sum of Table-2 (6048)* is Khufu’s inherent value for the number of feet in a nautical mile, and use that number, which we will now call a Khufu mile, to calculate the distance around the Earth at the equator, we obtain a distance of precisely 21600 Khufu miles.

i.e. The Earth’s equatorial circumference is equal to Khufu’s
perimeter (in feet), times the scale factor, divided by the number of feet per Khufu mile.

(4 • 756 ft) • (43200) / (6048 ft./ kfu.mile) = 21600 kfu.mile.

There have been eighteen copyrighted tables developed thusfar, which are the subjects of this treatise and the author has elected not to display them with these excerpts.

If you would like to read about the Author or reviews of the book, you may visit the WebPages provided by the publisher at:  

If you would like to contact the Author - Joseph Turbeville, his E-mail address is:  

---

"autographed copies available from the author" - A Glimmer of Light From the Eye of a Giant:Tabular Evidence of a Monument in Harmony with the Universe.

$14.95 US Dollars (plus $2.50 postage and handling inside the USA -- $3.75 outside the USA) Send check or money order to Joseph Turbeville -- PO Box 614 -- Hayesville NC 28904.

Please provide name of the person to whom it is to be autographed, and a proper mailing address.

 

 

http://www.gizapyramid.com/turbeville.htmjosepht@tri-county.main.nc.uswww.trafford.com/robots/00-0065.html