The Great Pyramid of Giza is the single most awe inspiring terrestrial achievement of mankind. It has inspired the great questions upon individuals and civilizations for millennia, while at the same time, offering its subtle answers in plain sight. As the greatest "wonder of the world," it has been thoroughly researched, measured and analyzed. Countless people of extreme talent and intellect have devoted their lives energy toward solving this structure's many riddles, and nearly every human to bear witness to it has wondered of its purpose. Even after thousands of years of scrutiny, the pyramid continues to unravel fantastic new correspondences to the dimensions of nature, as well as the question "how?!"
Yes, this article is just another shot at penetrating this great mystery and the insights within are not entirely my own. I stand upon the shoulders of all others, trying to capture sight of its light. However, you will find novel insights in my article below, and perhaps you will find greater understanding as to why so many correspondences exist within the symphony of "coincidence" that is the Great Pyramid. I intend to keep this a living document as marvelous information tends to flow continuously out of the analysis of this geometry and simply may not be captured in a single effort of composition.
To Square the Circle
There has been a fundamental problem that has been juggled throughout human history. It is as if the answers are lost and found again, to be lost and found again, over and over throughout time. It can be traced threading through most ancient civilizations and on up through present day. The history of this question is virtually the history of human mathematics and our intellectual achievements as a species. During the gold ages of history, such as the age of the pyramids, the problem and its solution are revered. This problem is known as the "squaring of the circle," or the "quadrature of the circle" and it concerns the composition of a circle of the same circumference as a square's perimeter (the question is also posed to the composition of equal areas.) Ultimately, a definitive method is sought that may achieve this feat in a number of steps.
One of the many purposes behind this question is, "how do you resolve the universal shape of the circle (composed of the "irrational and transcendental number" Pi) with the tangible shape of the square?"
The nature of Pi (the ratio between the diameter and circumference of a circle) has always perplexed the thoughtful- it is very much the bridge between 1 and infinity. It's numerical value never ends and so mathematicians determine it cannot be computed. They seek a definitive mathematical point as a square would provide, but cannot find it in the infinite resolution of the constant ratio of Pi.
The circle is simply not a polygon. No whole number other than one rules it - it is all whole numbers. Its continuous circumference may be subdivided without end and thus every order of number may fit within it, just as every whole number may be divided by 1, but none other than 1 may define it. This is in the same line as saying no 2 whole numbers in relation (giving a ratio) may divide into all other numbers within infinity evenly. And yet, there are ratios that indeed come about naturally which do define the characteristics of a circle along with other seemingly impossible mathematic feats concerning infinity. They are most often computed as the convergence of an infinite series of division, or as the mathematical result of other geometric constants in relation. These are the constants and they are our modern day mathematical treasures.
I myself was always a little perplexed as to why the "squaring of the circle" was given so much significance. After all, there are infinite polygons. Why not the "pentagoning of the circle" for instance? The question seemed loaded... It is as if the question itself is just as important as the answer. And it is in the context of history, for as long as people remembered to ask this simple question, they will be guided towards nature's most elegant solution... this is where the story of the Great Pyramid begins.
The Beginning of Geometry:
I assume most readers who find themselves to my website are aware of the geometric construct most commonly known as the "Vesica Pisces." This is the intersectional dimensions of two circles sharing a common radius- the circle in equal relation to itself. This could be considered the beginning of geometry, harmonics and mathematics; as the first tilt of balance upon the compass, it is essentially a first step in the correspondence of the continuum of space and dimensional relation. The poetry that this shape commands deserves no end; entire religions have been formulated to expand upon it through allegory, and in science and mathematics, it is quintessential whether acknowledged or not.
These are some basic measures concerning the Vesica Pisces. Notice how the first square roots expand from its core positions; numerous other "basic" ratios could be gathered if taken further. Also notice that a Vesica Pisces composed of circles 1/3rd the size (in green) of the original, would fit within the common radius of the original (in red.) What is important to grasp here in advance of the rest of this article, is that this shape is effectively a diagram of the interrelationship of singularity, duality and trinity- two circles and a common radius/ duality and neutrality/ 3 dimensional space, or musically speaking, the fundamental tone, the octave and the triangulation, or 3rd overtone of the octave. The holy trinity. It is no wonder why we called this "sacred geometry."
The Vesica Blueprint
Perhaps the Great Pyramid, in all its impenetrable mystery owes its basic blueprint to the Vesica Pisces? Perhaps the Great Pyramid is full of remarkable mathematical correspondence not because it is an abstract and random act of untraceable (or alien) genius, but because its core concept emerges from within the dimensions of this first act of nature?
Here we see how an extremely close approximation of the height to base relationship and slope angle of the pyramid may be found by tracing the positions of a Vesica Pisces placed within a Vesica Pisces. Remember, this represents 1/3rd, or 33.333... %. The corner slope view, or diagonal length to height ratios also fit within this same geometry. Again, in terms of ratios and harmonics, the fact the Great Pyramid design comes about as the relationship between a Vesica Pisces and another a 3rd of its size, implies that the structure is in essence about the triangulation of the "fundamental tone."
This relationship as far as I am concerned is the most critical concept in mathematics as well as the harmonic laws dictating energy transfer on a physical level. It surprises me not that it is given prime significance throughout history's philosophic institutions. The fundamental tone, (or any vibrating medium's principle oscillation) when it is self divided via the harmonic series, finds the first new tone at the 3rd overtone, which is an octave and a perfect fifth of the fundamental. As any student of music theory knows, the perfect 5th is the most harmonious tone amongst all others apart from the octave, and through the circle of fifths, all western music theory may be derived. Many have attributed this most harmonic and eternal relationship as the holy trinity.
Yet there is another critical function of triangulation which is not as commonly recognized, much less revered. The equilateral triangulation of the octave (which essentially produces the tonic, major 3rd and minor 6th intervals) is the principle act of triangulation amongst all ascending and descending wavelengths- it provides us with an inherent value of Phi- the "golden ratio." Phi is the all important ratio- the ratio of 1 to itself! This fact is critical to understanding magnetic currents, electromagnetic field mechanics and induced distribution on all scales of our continuum. This is not simply fancy number games we are talking about here- this is critical information that pertains directly to natural energy principles, or any applied technology that hopes to make use of them.
Is this also part of the message of the Great Pyramid?
-I encountered this function of Phi throughout my research into light refraction, harmonics, color theory and the groundbreaking magnetic field theories of Jon DePew. I go in to much greater depth in this article-
https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization which is largely based on Jon DePew's work http://www.coralcastlecode.com/
-Also, it seems very rare otherwise, but I have encountered much discussion of the importance of 3rds and 6ths in the literature of "sympathetic vibratory physics" from John Worrell Keely and his contemporaries such as Dale Pond.
A chart of the minor 6th, major 3rd and tonic relationship which produces phi ratios.
An example of the phi ratio as a principle geometric relationship between triangulation and the octave.
The link between the 6ths and Phi described by Dale Pond.
The ancient canon of geometry and number embodied by the pyramids lived on within countless subsequent philosophies and religions. Jesus Christ for instance is often depicted within a Vesica Pisces a 3rd the size of a larger Vesica Pisces it is positioned within, as he is here in this cathedral frieze.
Now in regards to the Great Pyramid, my calculations approximate that these angles equate to about 51.61 degrees to the average measured slope angle of 51.84 degrees of the actual pyramid's base to height angle, and 41.8 degrees to the 42 degree measured angle of the diagonal slope. That places this basic blueprint to within 99.5% accuracy of the actual structure, which ultimately incorporates a variety of slightly deviating angles and measures into its construction, (which we will get into.)
The difference between angles in the Vesica blueprint and the actual structure are barely visible at the resolution in this image above.
Thanks to Rich Jarvis for helping me verify these measurements. Please check out his "Golden" page:
While this shape provides us with an extremely close approximation of the actual structure, as well as endows us with important dimensional context, it is clear another design is more specifically at work. Nonetheless, the Vesica Pisces is indeed a central theme which I find to be essential to comprehension of the Pyramid.
Fun fact, the first time I became aware of this relationship was when I came across the solo album "Green" by Steve Hillage, most famously of the 70's prog band "Gong." It's a pretty groovy album, released in 78. Check it out, https://youtu.be/1cvZGqSZsic The fact that he titled his album "Green" and put this geometry on the cover is perhaps a wink across time between those in the know. If you want to learn more about the color green, and color in general, check out my article about light: https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization
Unraveling the Dimensions
Let us consider the ratios found among the measurement of the structure itself. Many surveys have been carefully conducted at the ancient site which were able to discern the most probable original dimensions of the structure. In the image above we have the result provided by the J.H. Cole survey that was completed in 1925. As you can see, there are slight deviations in many of the core portions of the structure. This could potentially be a result of human error or the physical limitations of the original builders (and even then their abilities and accuracy would still completely boggle the modern mind.) However, high level mathematical analysis conducted by many modern researchers are effectively adding credence to the possibility that these slight deviations were purposeful and intended to encode an even higher echelon of a holy numerical cannon. But that is no place to begin.
By simply averaging out the slope angles we can obtain the overall and ideal ratio of the structure. This would result in a slope angle of 51.84 degrees. With this value, upon the face of the pyramid, we strike gold- the guiding measure of the pyramid is revealed.
By taking the averaged distance from the centers of the pyramids base lengths to its apex and compare it to half of the averaged pyramids base length, we find an approximation of 1 to phi- together with the pyramids side length as the hypotenuse, we have the "golden triangle."
The "simple answer" to the Great Pyramid is that its design is ultimately based upon this "golden triangle," which makes up the face, and the square, which makes up the base. 8 right angle golden triangles with a height of Phi and a base of 1 are tilted from the sides of a square to meet at a common apex. This produces a height equal to the square root of phi!
There are of course 4 principle shapes to the pyramid when considered as a whole in all 3 dimensions. The square base (looking downward from directly above for instance,) the diagonal dimensions, (looking directly from the corner to see two sides at once,) the cardinal dimensions (looking directly at any single face of the pyramid which all happen to be perfectly oriented in the cardinal directions,) and the face dimensions (looking directly at a face triangle if it were laid out flat in front of you.)
As depicted above, these principle measures can all be laid upon each other in 2d, or put together to reveal the 3d construction, both are effective methods at discerning their mathematical ratios. These are the core dimensional components necessary to understand the pyramid further.
What do we see here?
To me, I see a square (a power of 2) coming to a single point by means of the golden triangle/ function of Phi. Again, triangulation of the octave, at the ratio of one to itself.
It turns out this function of phi results in an explosion of additional mathematical constants!
Something to note- it was Jon DePew who first described Phi as a flexible function with much more to it than the numerical value of 1.618 that we limit it to. He describes that it is more accurate to consider phi as dividing something equally- like dividing a gradient of wavelengths equally as we described earlier. I am reminded of his words when I consider the Great Pyramid. We find that Phi is a guiding principle from out of which, all of mathematics seems to explode and interconnect and at the same time be equalized.
A Treasure of Constants
Upon even further analysis of the ratios between the different portions of these specific shapes, researchers have been continuously discovering mathematical treasures. In the diagram below are listed 12 mathematical constants! Some of these have been known and recognized as being attributes of the pyramid's measure for quite some time, others were discovered quite recently. Several more constants are sure to be, and have been found beyond this list. Also, the ratios can be seen to describe not only mathematic constants, but also the relationship between various units of measure used throughout human history, such as the Royal Cubit, the Meter, the Foot and several more!
Several of these discoveries may be attributed to the fantastic and contemporary work of Alan Green. Check him out and let him go into much more detail about his work in this field:
The constants listed above cover a wide array of seemingly disparate mathematic disciplines. As discussed, Phi is of course there and the square root of phi is there, as well as the inverse of phi (phi-1.) As you should also expect, Pi is there. The square roots of 2, 3, 4, 5 and 6 are all there. Even more obscure constants appear too. Brun's constant (B2) which has to do with twin prime numbers is there (this value is also found as the hypotenuse of the golden triangle.) Euler's constant which is the limiting value of the natural logarithm is there, as well as the Euler/ Mascheroni constant which is the limiting difference between the harmonic series and the natural logarithm. Finally, the Tribonacci constant, which is the limiting value for the Tribonacci series (like the Fibonacci series, but using 3 numbers instead of two in order to sum up the following number.) There are certainly many more constants to be found, the Great Pyramid is the gift that keeps on giving.
Words fail to describe the magnitude of how amazing this is mathematically... and we have truly only begun to scratch the surface of the profound depths of correspondence this structure encodes. To think "mainstream" Egyptologists often argue the pyramid was a mere tomb and question its higher mathematical purpose... Even today we lack the mathematical finesse of these ancient people! Contemporary mathematicians and theoretical physicists seek the great prize of a unified theory by searching through their extravagant messes of calculative imagination, and in doing so, they overshoot the divinely simple truth completely. In a way, the answer has lain hidden in plain sight for thousands of years, written in a language that never changes. The ancient masterbuilders erected a temple in the dimensions of their unified equation and set it in stone to span human future and history; a time capsule of truth for all with the eyes to see.
Now ask yourself, did the ancient masterbuilders of this structure truly know of each and every one of these mathematic constants, or is this design demonstrating an inherent unity in the seeming independence of all these constants arising from this principle function of phi which we find guiding its measure?
Or perhaps both?
P.S. Speaking of Masterbuilders, and in keeping with the Steve Hillage music theme, I can't help but recommend: https://youtu.be/kFSNs9GQe_4
The Circle Stands Squared
So getting back to that ancient problem posed since time immemorial we talked about earlier... that curiously loaded question that seemed to receive strange importance in the context of history... Turns out that within its solution is described a unified functioning and fundamental dimensional interdependence of the principle mathematical constants and our number system. The Great Pyramid is the solution! The square root of Phi is the radius of the circle to a square with a side value of 2.
This is truly a holy science, make no doubt about it. Worthy of immortalizing into stone, a beacon of truth for all histories to come.
This function goes deep. All dimensions it describes in total have important mathematical relevance, as exemplified by the Great Pyramid's measures we reviewed earlier.
As an example of how this function works, let's look into how the phi ratio plays its role. By placing the 4 key pyramid dimensions in relation, I was able to document up to 42 linear instances of the Phi ratio! (Before I got tired of counting all of them and stopped.)
Here I make use of the inscribed and circumscribed circles of each of the pyramid shape and find 9 unique vertical instances of phi.
Here are horizontal instances of phi from the slope and diagonal angles. Notice how the Vesica Pices when placed in relation to the pyramid dimensions is also a generator of this ratio.
Instances of phi from the face angles.
Sloping instances of phi in relation to the Vesica Pisces.
Sloping angles of Phi in relation to the inscribed and circumscribed circles.
Now let us look at the squared circle shape in relation to its inscribed and circumscribed circles (these are circles that touch the inside and outside of the square.) Let us take all these dimensions and polarize them. This is what I am doing as far as I am concerned when I create the Vesica Pisces out of them by drawing two squared circles with a common radius and letting their shared center line up with the axis of the original lone squared circle. See diagram below.
Phi relationships are throughout, as nature and the ancients promised.
Now, meditate on this:
Speaks for itself right?
At least it does to some ;)
The Golden Angle and Harmonic Law
If one were to distill the universe of numerical and energetic law into fundamental concepts, it could well be argued that the two most principle would be the "harmonic series" and the golden ratio. Could it be demonstrated that there is a relationship between these concepts? Well, one of the things I love so much about geometry and math is that truth so often does reveal itself through multiple dimensions, and in very intuitive ways.
A measurement originally carried out by Viktor Schauberger was recently brought again to my attention and its relevance to the great pyramid, (and many of my own recent findings regarding electromagnetic scaling and distribution) was abundantly clear.
Viktor drew out a hyperbolic funnel by mapping the relationship between frequency and wavelength of the harmonic series. This essentially charts the balance between expanded wavelength of lower energy and contracted wavelengths of higher energy. This is also describing the magnetic and gravity potentials inherent in the "inverse square law." (Consider how the gravity field potentials of masses are often represented by funnels such as the one below, and also to depict the spacetime curvature of relativity. The orbits of planets of course are also plotted as hyperbolic in relation as well.)
Now if we cut this funnel at 51.84 degrees (the slope angle of the Great Pyramid) we are left with the shape of the "golden egg" whose proportions are 1 to Phi.
This is a truth I will not interject too many of my thoughts into as it is worthy of meditation in your own right. I will say simply that the golden ratio is alive as a unity throughout the world of infinite numerical form, and nature corresponds.
These basic functions of mathematic and geometric dimension we have discussed above do not simply translate into philosophies existent in the brain and mind alone. They manifest physically in nature and they manifest physically in energy. On all scales energy is being divided, induced and rhythmically distributed equally- so that no thing need be created or destroyed.
The scales of the Earth and the moon for instance.
And electromagnetic refraction and induction.
The function of phi is at work. It is the secret of light.
Here is an article I wrote about these same values I measured in spherical refraction.
Where does it go from here?
Believe it or not, we have only scratched the surface. While these are the most critical points, we have merely discussed the ABC's of the pyramid and of the functions guiding its design. We have only so far analyzed the averaged ratios, we have not reviewed the higher mathematical canon that is revealed in its units of measure and the finer intricacies of its internal features. We have not jumped into the rabbit hole of its spectacular geophysical, astronomic and physical constant correspondences, only hinted at in the images above. Nor have we speculated as to how the hell this pyramid was constructed in the first place (this is where I myself throw my hands up in sheer bewilderment!)
It is clearly the core dimensional functions of Pi and Phi however which are most specifically immortalized in the pyramid. This is the fundamental knowledge and wisdom which enlightened the minds of our great ancestors thousands of years ago and which led them to develop true mastery and achieve a golden age we could only dream of...
To be continued...
P.S. There are many more authors and researchers who have compiled great insights and highly compelling breakdowns of the Great Pyramid measures. I will recommend some researchers below in case you are not familiar with them and want to study this subject matter much further. Please feel free to drop your own links in the comments below!
- If you have not already encountered John Michell's work, start here! John's work has inspired innumerable researchers into the depths of this subject matter.
-As mentioned previously, Alan Green has recently uncovered many of the constants and units of measure correspondences we reviewed above- be sure to review his remarkable work! Truly a gift to humanity and a revelation of knowledge past.
-I recently came upon this Youtube channel called SGD. It is the work of Alan L from Australia (what’s up with you Alans?!)Alan has compiled an insane amount of information into the ancient numerical canon and has put together hours of video detailing the Great Pyramid specifically. HIGHLY RECOMMENDED! https://www.youtube.com/channel/UCtf-VP785ViwA-Y6VVczoPw/videos?view=0&sort=dd&shelf_id=9
-Scott Onstott- www.secretsinplainsight.com
- Rich Jarvis - https://www.facebook.com/WelcometotheGoldenPAge/
-Gary Osborne- http://garyosborn.moonfruit.com/#/sacred-earth-pyramid-geometry/4572231179
And many more...