I knew that before modern satellite technology, triangulation was the means used by land surveyors to determine an unknown point from the angles of two known points. Could the ancient architects have perhaps built some form of triangulation into the Giza pyramids that could act in some way to allow the pyramids to “point” to a secret location? If so, then how might this have been done?
Long before embarking upon my Giza adventure I had spent many months on my home computer drawing all manner of lines from all manner of significant points on a survey drawing of Giza. It eventually became apparent to me that such an exercise was entirely futile. There were simply too many possibilities pointing to too many different potential locations. If the pyramids had been designed in some way to triangulate to a particular unknown point, then it stood to reason that the rationale employed by the designers would ensure that any such triangulation technique could result in only one possible unique location being identified. But how could the three pyramids be used collectively to indicate just one unique geographical location? Once again I was stumped.
But it often seems to be the case that just when you think your mind has hit a stone wall, that is exactly the tonic it needs, for in hitting that wall it completely cleared my mind of the cluttered debris of redundant ideas and dead ends that had been rattling around for months, allowing me to start again from scratch. However, one thought remained very firmly fixed in my mind: the words of Djeda—“found by three”; these words were never far from my thoughts. “Found by three.” The three Giza pyramids seemed the obvious “three,” but could there be something else, some other fairly obvious “three” that related to triangles that I was not seeing?
THE PENNY DROPS
Up until that moment I had never been a great believer in serendipity, but as I grappled with this seemingly insoluble problem of finding a means by which all three Giza pyramids could collectively be used in a unique manner to somehow indicate a single geographical location, my young son asked me a completely innocuous and random question about triangles for a school math project on which he was working. He wanted to know how to find the center of a triangle. The question was simple enough, and at first there was no spark, no blinding light, no great epiphany. That would happen some minutes after his simple question had time enough to percolate through the filters of my mental reasoning.
I began by explaining to my son that, unlike a circle or a square, a triangle can actually have many different “centers.” Today we know of 5,389 different ways to plot unique points (centers) within any particular triangle, but in the ancient world only the three simplest triangle centers were known.
Eureka!
My moment of epiphany had arrived.
There it was; in the ancient world only the three simplest triangle centers were known! Finally, the light was switched on.
THE TRIPLE CENTROID
The idea was simple enough. Each of the three main pyramids at Giza might represent one of the three triangle centers that were known in the ancient world—three triangle centers that today we know as incenter, barycenter, and circumcenter (figures 2.1, 2.2, and 2.3).
1. The Incenter
This point requires a circle to be inscribed within the triangle whereby the perimeter of the circle touches all three sides of the triangle. The center of the inscribed circle is then plotted, and this point becomes the triangle’s incenter centroid.
Figure 2.1. The incenter centroid
2. The Barycenter
This point requires a line to be drawn from each of the triangle’s vertices to the midpoint of the opposite parallel. The intersection where the lines meet is plotted, and this point becomes the triangle’s barycenter centroid.
Figure 2.2. The barycenter centroid
3. The Circumcenter
This point requires a circle to be circumscribed around the triangle in such a way that its perimeter touches all three vertices of the triangle. The center of the circumscribed circle is then plotted, and this point becomes the triangle’s circumcenter centroid.
Figure 2.3. The circumcenter centroid
As stated earlier, each and every triangle can contain all of these different “centers” at the same time. But depending on the particular shape and orientation of the triangle, the different centers will fall at different relative positions within the triangle (sometimes even outside the triangle). In this regard we can consider the three centers of the three pyramids as each belonging to one of the three most ancient triangle centers, and together they could be used to reverse-engineer the unique triangle that contained these three centers; that is, we could use this understanding of the three triangle centers known in the ancient world and determine the unique triangle that matched the particular configuration of the three pyramid centers.
Reverse-engineering this unique triangle was not as easy a task as I had at first imagined, and it involved countless hours in front of a computer screen testing different-shaped triangles, trying to find a unique triangle whose three inherent centers (incenter, circumcenter, and barycenter) matched the relative disposition of the three pyramid centers. Finally, after many nights falling asleep at my computer desk, I eventually found a triangle (figure 2.4) whose three latent triangle centers (incenter, circumcenter, and barycenter) matched the relative disposition of the three centers of the Giza pyramids.
Figure 2.4. The Giza triple centroid triangle
What is also interesting about this triple-centroid construction is that the cardinally aligned “cross” of the incenter and circumcenter triangles naturally aligns with the lines of the concavities of G1 and G3 and seems to offer an explanation as to why G2 was entirely devoid of these concavities because, being the barycenter of the reverse-engineered Giza triangle, there would be no circle and therefore no cardinally aligned cross to indicate the circle’s center. As such, it rather seemed to me, at that point, that the architect of these pyramids had perhaps placed the concavities into G1 and G3 so as to present a subtle hint (the cardinally aligned cross of the concavities alluding to the center of a circle) toward their latent triangle centers in order that these might be used later by someone to reconstruct or reverse-engineer this unique, grand triangle over a plan of the Giza pyramids. And if we consider the two lines that converge at the apex location, we find that both these lines are oriented generally northeast and southwest and have the same angle (figure 2.5)—just as the Emerald Tablets of Thoth indicate to us. These “tablets,” which form part of the Corpus Hermetica, comprise ancient wisdom texts believed to have been written by the ancient Egyptian god, Thoth the Atlantean, before the Flood.
Figure 2.5. The Great Giza Triangle has two sides at the same angle: 34°.
So here we have two lines drawn toward the same direction of the Giza plateau and at the same angle—but to what end? What exactly would be the point of such a hidden, grand triangle? Well, not to place too fine a point on it, but the point is the triangle’s apex—its endpoint! This unique triangle actually acts like an arrowhead or pointer that targets a very specific location to the southwest of the Giza plateau on the edge of the desert—the very place I was now headed.
As the Emerald Tablets foretold, “Dig ye and find that which I have hidden. There shall ye find the underground entrance to the secrets hidden before ye were men.”1
Having identified the apex location of the grand triangle on a map of Giza—an apparently inconsequential area to the southwest of the Giza pyramid field—I knew at once that I simply had to get myself to that location. I knew not, of course, what I would find if and when I ever got there, but it seemed to me, based on the legends of the secret chamber, that it would be “found by three.” And the unique nature of the Great Giza Triangle, which itself was “found by three” (i.e., the three pyramid centers corresponding to the three triangle centroids), would be as good a place as any to begin such a search.
But my trip to this remote location in the Egyptian desert would also become something of a pilgrimage, a journey to pay hom
age to the remarkable builders of these truly awe-inspiring structures. To that end I had taken with me a small pyramid made of Scottish granite—small enough to sit in the palm of my hand. At the apex location I would place my small granite “gift to Osiris” and, in homage, would speak a few words from the “Hymn to Osiris.” This hymn contains the most complete account of the Osiris myth ever recorded by the ancient Egyptians, recounting his death at the hands of his treacherous brother Seth and his resurrection and vindication as the true ruler. In reciting these immortal words I felt as though I would be following in the steps of the ancient Egyptians who venerated this god of rebirth and regeneration; I would also be acknowledging and honoring the tremendous achievement of this ancient people who, by their blood, sweat, and tears, ensured their own (and our) future. And by placing my small pyramid offering at the precise spot the geometry of these great monuments “point” us to, it may also serve as a message to someone who, perhaps ten thousand years from now when our civilization has perhaps been decimated and lost, might understand the same geometry, seek out this very spot, and find this small pyramid that would tell them something of our own civilization.
THE MYTH OF OSIRIS
I’d been traveling along the desert road for about a half hour and had now almost reached the vista point. About six or seven buses were bunched together in a makeshift bus park while dozens of tourists milled around taking snapshots of the pyramids, which thrust out of the desert sands about a mile in the distance. As I turned the sharp bend into the bus park’s entrance, from the corner of my eye I caught a glimpse of an Antiquities Guard near the boundary wall at the far side, mounted on a camel, having his photograph taken with some tourists and more than happy to relieve them of some baksheesh for his trouble. Or perhaps it was the somewhat unsettling sight of his Glock handgun that compelled the tourists to part with their cash.
This was awkward and precisely the kind of situation I had hoped to avoid. I didn’t want to continue on my journey with the guard so near and so able to observe my movements. Not that I was doing or even about to do anything illegal, but it would have looked somewhat peculiar, a lone figure heading out onto the desert road on foot, and would surely have piqued the guard’s curiosity and no doubt his attention, which I could well have done without.
Thus, for the next half hour or so I had to stay put and content myself with some sandwiches and my bottle of water—killing time. It was also a convenient opportunity to join the frenzy of pyramid shooting. While this particular aspect of the pyramids—spread out north to south—was truly magnificent, it was not nearly as spectacular a view as the iconic, jaw-dropping, east-west panoramas to be seen from the vantage points to the south of the Giza pyramid field. From the location here the pyramids seemed somehow disjointed, like pieces of a gigantic geometric puzzle that had become scattered and disconnected and that needed to be picked up and reassembled (figure 2.6).
After having taken the third “pyramid-in-my-hand” photo for some grateful American tourists, I overheard the crackling of the guard’s radio. He took the radio from his belt and spoke into it briefly before signaling with a brush of his hand, “No more photos.” Before long, and with a considerable sense of relief, I watched as he exited from the bus park on his camel, heading out across the desert sand in a southeasterly direction—opposite to where I was headed. I didn’t waste any more time. I quickly packed my things and, with one final check that the guard was fully out of sight, made my way once more onto the dusty road.
A few hundred yards later the road took a sharp turn, heading almost exactly due south. In the distance I could see the rise of a small hill, beyond which was my goal. The feeling of excitement and exhilaration was building within me with each passing step. As I looked to the pyramids in the distance behind me, something rather remarkable was occurring—as I reached the point where I was almost perfectly in line with the diagonal of the three pyramids, the wide gaps between them had completely vanished, giving the illusion that the three individual structures had morphed into one giant, unified body. In this I was reminded of Plutarch’s tale of Osiris and Isis whereby Osiris (the ancient Egyptian god of rebirth and regeneration), having had his body cut into sixteen pieces (some versions of the tale say fourteen pieces) by his evil brother Seth, who then scattered them all across the land of Egypt, was made whole again after his wife (and sister) Isis found all the body parts (with the exception of one) and pieced them together again.
Figure 2.6. The Giza pyramids (looking east). Photo by Scott Creighton.
I began to wonder if there was in fact a kernel of truth in this ancient myth, whether it could be possible that this story was actually an allegorical tale pointing us toward a fundamental truth that the body of Osiris that had been cut into sixteen pieces and scattered across the land was not meant to be understood in terms of a human body but was perhaps a metaphorical reference to the early, giant pyramids acting as the body of Osiris, much in the same way that a Christian church today represents the allegorical “body of Christ.” And further still, could it be that the one piece of the “body” we are told from the myth that Isis could not find may be an allegorical reference to a hidden part, a subtle clue to a hidden vault somewhere deep underground, awaiting discovery—the legendary hidden chamber of Osiris?
This may not be as radical a thought as it may at first seem. The idea that the scattered “body of pyramids” (i.e., the first sixteen or so pyramids built by the ancient Egyptians at Abu Roash, Saqqara, Meidum, Dahshur, and Giza) may represent (or may have come in later times to represent) the allegorical body of Osiris finds some support in our earliest religious texts, the ancient Egyptian Pyramid Texts, in which it is written, “This pyramid . . . is Osiris . . . this construction . . . is Osiris.”2
This notion is given further support in Frank Cole Babbit’s translation of Plutarch’s Isis and Osiris, in which we read, “The traditional result of Osiris’s dismemberment is that there are many so-called tombs of Osiris in Egypt; for Isis held a funeral for each part when she had found it . . . all of them called the tomb of Osiris.”3
While it may have been believed by some later historians such as Plutarch and Herodotus that these early pyramids (along with the hundred or so much later pyramids) had been conceived and built as tombs, there is considerable evidence—presented in the next chapter that raises some serious questions about that assertion. What is absolutely certain, and for which there can be absolutely no doubt, is that clearly intrusive burials have been recovered from a number of the earliest pyramids. And, by the same token, what is clear also is that not a single intact burial of an ancient Egyptian king has ever been recovered from any of these first pyramids (or indeed from any pyramid in any age). Indeed, the only fully intact burial of an ancient Egyptian king ever found was that of Tutankhamun, who was buried in a deep, underground tomb (not in a pyramid) in the Valley of the Kings.
The concept of pyramids as arks or recovery vaults for the kingdom (containing all manner of seeds, tools, pottery, etc.) could not be better symbolized than by the ancient Egyptian god Osiris, their god of agriculture and of rebirth. The pyramids contained, after all, the means by which the kingdom hoped to recover should the worst effects of “Thoth’s Flood” come to pass. These “dismembered body parts” (i.e., the individual pyramids scattered along the length of the Nile) represented the agency through which the recovery or rebirth of the kingdom could occur.
In essence these first scattered pyramids along the Nile Valley were Osiris (i.e., his body cut into sixteen parts), just as the ancient Egyptian Pyramid Texts and Plutarch’s Myth of Osiris inform us. As such it should be of little surprise then to find that when plotting the individual locations of the first, giant pyramids onto a map of Egypt, what we find is a crude “matchstick” outline drawing of the classic Osiris figurine (see figures 2.7a–e), complete with the royal regalia of the distinctive three-pronged Atef Crown of Osiris and symbols of power, the crook and flail.
These images
demonstrate the locations of the pyramids listed below with the name of the king Egyptologists believe constructed each pyramid (its location in parentheses), and which were constructed on the high plateaus along the lush green Nile Valley (Osiris is often painted with a green body depicting vegetation and rebirth) and are believed by Egyptologists to have been completed in the following order of construction.
Djoser (Saqqara)
Sekhemkhet (Saqqara, unfinished)
Khaba (Zawiyet al-Aryan, unfinished)
Sneferu (Meidum, farthest south)
Sneferu (Dahshur, the Bent Pyramid)
Sneferu (Dahshur, the Red Pyramid)
Khufu (Giza, with four satellite pyramids)
Djedefre (Abu Roash, farthest north)
Khafre (Giza, with one satellite pyramid)
Nebka (Zawiyet al-Aryan, unfinished)
Menkaure (Giza, with three satellite pyramids)
Figure 2.7a. The first pyramids outline the god Osiris.
Figure 2.7b. Locations of the first 19 pyramids built by the ancient Egyptians along the Nile Valley (inludes 3 unfinished pyramids).
The Secret Chamber of Osiris: Lost Knowledge of the Sixteen Pyramids Page 5
