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The Great Pyramids

The Great Pyramid of Giza (Egypt) is traditionally attributed to the Pharaoh, Cheops, but recent evidence has strongly suggested this last remaining of the Seven Wonders of the World is doubtless much older than any Pharaoh of Egypt’s Old Kingdom.  Furthermore, the assumption by old Paradigms and so-called authorities that the Great Pyramid was a tomb for a vain glorious Pharaoh is in even greater disrepute.  Laurence Gardner [1] has noted, for example, that there has never been a single tomb of an Old Kingdom pharaoh discovered with a body still in the alleged tomb.  As such, this would make for a very lousy means of entombment, if the bodies kept disappearing or being ripped off <g> by thieves!  [Okay folks, it's a wrap!]

More information on this topic can be found at the Halexandria Forums,

in particular, the connection to the Aztec Stone Calendar.

The antiquity of the pyramids of Giza, their debatable purpose (whether a  tomb or something far more profound), and the fact they were designed on the basis of a sacred, hermetic geometry, makes for considerable intrigue.  Scholars have, in fact, labored over the Great Pyramid of Giza, and in the process have discovered a host of marvels.  For example, the builders almost certainly knew the precise circumference of the Earth and the length of the year to several decimal places accuracy.

        This includes the Sidereal year (365.2564 days between two sightings of the same star before and after the earth’s orbit), the Anomalistic year (365.2599 days of the earth’s sun orbit), and the Solar year (365.24 days between two successive autumnal equinoxes).

The Great Pyramid of Giza has been shown to be an almanac capable of measuring the length of the year to an accuracy of 365.2422 days -- rivaling the accuracy of a modern telescope.  The ancient architect(s) may also have known the mean length of the Earth’s orbit around the sun, the average distance of the Earth from the Sun, the specific density of the planet (and thus the weight of the planet), the precession of the equinoxes (which defines the current era as the Age of Pisces), the acceleration of gravity, and the speed of light.  In fact, as a simple, precise, and virtually indestructible surveying instrument, the compass point of the pyramid is so finely tuned to north that modern compasses use it for a reference.  The Pyramid’s location also serves as a geodetic marker for the geography of the ancient world - being located at the geocentric center of the earth’s land mass.

The Great Pyramid also incorporates in its sides and angles the means for creating a highly sophisticated map projection of the northern geohemisphere, and as such correctly incorporates the geographical degrees of latitude and longitude. It is also a celestial observatory from which maps of the stellar hemisphere can be accurately drawn, and along with the other two Giza pyramids replicates the exact positions of the three stars in the “belt” of the Constellation Orion.  Finally, there is an example of The Golden Spiral, whereby the three pyramids and the Sphinx are interlocked and thus situated by design.

The hemispherical map projection is particularly intriguing.  The apex of the Pyramid, for example, corresponds to the geographical pole, while the perimeter of the Pyramid corresponds to the equator, both in proper scale.  Each flat face of the Pyramid was designed to represent one curved quarter of the northern hemisphere (a spherical quadrant of 90°).  This is more difficult than one might imagine, for in order to project a spherical quadrant onto a flat triangle correctly, the arc, or base of the quadrant must be the same length as the base of the triangle, and both must have the same height.

This can only happen in a pyramid if the slope angle allows for a p relationship between the height of the pyramid and its base.  In this relationship the side (S) of the Great Pyramid, divided by twice the height (H) must equal p divided by four, i.e.:

S / ( 2 x H )  =  p / 4  

The slope angle, a, between the slope of the pyramid’s side and the horizontal is given by tan a = 2 x H / S = 2 x 480 feet / 754 feet, such that a = 51.853318324... °. This angle becomes extremely important in the construction of pyramids, great and otherwise, and we will return to it shortly.

        The slope angle is intriguingly similar to 360°/7 = 51.42857142857...°  This similarity is discussed in more detail in Nines.

It is clear that the builders of the Great Pyramid knew their Sacred Geometry, as well as the importance of the Golden Mean.  By choosing the proper dimensions, they managed to ensure that the area of each face of the Great Pyramid is exactly equal to the square of the pyramid’s height.  This is a nice trick, and is accomplished by choosing the slope of the Pyramid such that the apothem equals 1.618 times half the side of the base.

For example, if half the side of the Great Pyramid (S/2) is set equal to 1, the height of the Pyramid equals ÖF (F being the Golden Mean), and the apothem (the distance from the midpoint of a side, along the face of the pyramid, to the top) equals F.  In some respects, this is simply the Pythagorean Theorem where the square of the hypotenuse (F) equals the sum of the squares of the sides (1 and ÖF).

But wait a minute!  The slope of the Pyramid has already been determined by relating the height and side of the Pyramid’s base to p!  Suddenly, we are confronted with the fact that both F and p are involved, and in fact, the builders of the Great Pyramid have given us a way to relate p to the Golden Mean, i.e.:

p x ÖF @ 4

            The actual answer is 3.99616758... (which corresponds to an error of 0.0958%).

Clearly, the Great Pyramid’s architects knew what they were doing.  And there’s more!  When the Great Pyramid is viewed from the side, the laws of perspective reduce the area of the face (which is mathematically oversized) to the correct size for the projection.  Interestingly, this projection is exactly equal to the Pyramid’s cross section.  Thus what the viewer sees -- with the aid of perspective -- is the correct triangle.

Finally, in the early descriptions of the Pyramids, the measurements were in cubits, where the Great Pyramid’s apothem was 356 cubits and the base, 440 cubits.  If one divides 356 cubits by half the base, 220 cubits, we again find the Golden Mean.  The trick is to divide both 356 and 220 by four, in order to arrive at the ratio of 89 divided by 55.  Both being Fibonacci Numbers, the answer is 1.618 (i.e. F, good to three decimal places).

While thinking about this, it might be a good idea to take a quick side excursion to the Pyramid to the Sun in Teotihuacan, Mexico, which has very nearly the same dimension of its side (748 feet) as the Great Pyramid of Giza (754 feet).  Furthermore, the two largest pyramids at Giza have their peaks at the same elevation (i.e. the Great Pyramid is built on slightly lower ground).  This is also true at Teotihuacan, where the Pyramids of the Sun and Moon have the same peak elevation, but the Pyramid of the Sun is built on lower ground.  The big difference is that at Teotihuacan, the pyramid’s slope is given by:

S / ( 2 x H )  =  p / 3  

This fundamental variation leads to an approximate height of the Teotihuacan Pyramid of 357 feet, and a slope angle of  a‘ = 43.67929626...°.

        We might also point out: 1) 90° - a (Giza) = 38.146681676...°, a number strangely similar to 100f2 (38.1966011...), and 2)  tan a‘ (Teotihuacan) = F2 + F4 (within a 0.81% error).

This lower angle is not arbitrary.  The three Pyramids of Giza are the only pyramids in Egypt which have attained the steep angle of almost 52°.  All of the other, later Egyptian pyramids -- all of which are more recent, lesser, smaller, decayed, or collapsed -- were likely built by Pharaohs, but none succeeded in attaining the “perfect angle” of 52°.   

Not that they didn’t try, however.  Pharaoh Sneferu, early on, embarked on building steep angled pyramids at Dahshur and Maidum.  The latter collapsed, and the architects quickly changed the Dahshur pyramid to a safer angle of 43 1/2°.  This change in mid-construction resulted in a pyramid now known as the “Bent Pyramid”.

The fascination is that the 43 1/2° angle of the upper portion of the Bent Pyramid and all of the other pyramids of Egypt have been built at the same angle as the Pyramid of the Sun at Teotihuacan!  Furthermore, while an angle of 52° might have been derived from simply dividing 360° by 7, 43 1/2° has no such correspondence, and a simpler minded builder might more realistically have chosen 45°.

The fundamental lesson is that the pyramid builders were building to the specifications of Sacred Geometry.  And when they couldn’t make the ideal 51.853318324...°, they went for the less ideal, but still in The Golden Mean ball park of 43.67929626...°.

        These angles, by the way, can be directly related to F and p, by the following:

 tan a  =  ÖF  =  4 / p                   (Giza)

                        tan a  =  ÖF x (3/4)  =  3 / p          (Teotihuacan, et al)

Finally, before we leave Egypt, we might note that part of the legacy of the Great Pyramid architects is a means to calculate ever increasingly accurate values of p by use of the Fibonacci Numbers.  This is done by utilizing the formula given above, p = 6 x F2 / 5.  For example, for higher values of the Fibonacci series, e.g. 9,227,465 and 5,702,887, we obtain a value of p equal to 3.14164079... (vice 3.14159265...).

For further research, there is the book, Peter Lemesurier’s The Great Pyramid Decoded [2].  This classic even noted similarities of construction between the Great Pyramids, Stonehenge, and Chartres Cathedral (France).  The latter is fundamentally important with respect to the Ark of the Covenant, while Stonehenge is a masterpiece of astronomy and evidence of mankind’s very early understanding of the cosmos.  Lemesurier also describes a “timechart” included at the Great Pyramid of Giza, wherein is predicted the “total collapse of materialistic civilization” for the time period 2004 to 2023 (±3 years).  Obviously, 2012 A.D. is within these limits.

More information on this topic can be found at the Halexandria Forums.

Over and over, we keep discovering the truth of Mark Twain’s saying quoted at The Library of ialexandriah: “The ancients have stolen all our really good, new ideas.”

But for those interested in rediscovery, there are the Underground Cities, Harmony of the Spheres, The Fifth Element, 600 B.C.E, and Ages in Chaos.  Or simply return to the days of yesteryear, i.e. Sacred Mathematics, or The Lord of the Rings.

Other links include:  

            Alan Alford’s <http://www.eridu.co.uk/Author/egypt/giza.html>, an excellent website for information on the dating of the Giza pyramids, including the fact that the construction of the Great Pyramid might have been during different eras than the other pyramids and the Sphinx.  Alford maintains a degree of inconclusivity, which is refreshing.

            And <http://www.sacredsites.com/2nd56/378.html>, and even more speculative website -- but intriguing nonetheless.


Sacred Geometry         Geometry of Alphabets

Forward to:

Orion         Sirius         The Dogon Tribe         Underground Cities



[1]  Laurence Gardner, Genesis of the Grail Kings, Bantam Press, New York, 1999.

[2]  Peter Lemesurier, The Great Pyramid Decoded, Barnes & Noble, New York, 1977, 1996.





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