At present, I seem to be doing too much juggling for my own good. With one hand, I am working on the ultra-Herculean task of attempting to make sense of the larger layout of the Giza pyramids, while at the same time I have been tempted to start looking the engineering of Egypt’s ancient pyramid with the other.
The idea that the Great Pyramid was built using ramps, however prevalent the idea may be, manages to strike me as unlikely for a number of reasons and worse, to me represents the same lazy-minded, “lackadaisical” thinking on the part of many Egyptologists that has made such a demonstrable mess of ancient Egyptian metrology and mathematics.
Were I wiser person, I would probably avoid the subject of ramps and keep my eye on the task of understanding Petrie’s data for the placement of Giza’s major pyramids – indeed, the questions of how the pyramids were built, or even why they were built, really aren’t my area, as opposed to the question of what the pyramids are, metrologically, mathematically, geometrically or astronomically speaking.
Yet the minute we get beyond the question of how Cheop’s pyramid was built and into comparative studies of the anatomy of Old Kingdom Egyptian pyramids, the question of how inevitably tries to cross paths with the question of what.
The Bent Pyramid at Dahshur is one of the first things to come to mind here. The orthodox perspective often tries to attribute its novel “bent” design to a late course correction related to aversion of structural failure, even while a number of us “alt” researchers are able to come up with mathematical models that may suggest otherwise – that the “bent” shape may have been planned from the very beginning.
There is even a surprising amount of consensus among some of us, so that even while we may not agree on the precise specifics, we may be in general agreement about what some of the Bent Pyramid’s proportions represent – i.e., that the base perimeter of the Bent Pyramid in “modern” “Imperial” feet seems to represent the Earth’s circumference in “modern” miles.
This idea might be absolutely ludicrous even to my own sensibilities were geodetic data not peeking out of seemingly every corner at Giza.
Indeed, I often wish I didn’t have the excess baggage of trying to defend the prospect of the ancients possessing advanced and specialized geodetic knowledge about the size and shape of the Earth, when it seems like enough a battle already just trying to get some to consider the possibility that the ancients could actually do arithmetic better than is evidenced by a scant few generalized mathematical papyrii – but the appearance of this data in ancient architecture happens with a remarkable frequency that I cannot believe is mere coincidence.
In my writing over the course of the last few years, I have given many examples of how this geodetic data is expressed at Giza – yet we can almost guarantee that Egyptologists are having none of this whatsoever, and that it certainly isn’t likely to enter into any orthodox considerations of whether or not any “bent” pyramids show metrological or mathematical signs of planning and forethought, as opposed to their final proportions being desperate last-minute course corrections due to structural failures.
I have generally tried to avoid the subject of 3rd Dynasty Egyptian pyramids even though sooner or later addressing them is probably vital to an understanding of the history and evolution of ancient mathematical and architectural science – especially in the case of Sneferu’s pyramid at Meidum, yet now I find myself tempted to return to the subject of this pyramid, which to my reckoning remains shrouded in too mysteries, not matter how we try to look it at.
There may be something of a paradox in that good data projections might help to have an understanding of exactly what happened there, while an understanding of events surrounding the Meidum pyramid’s state might be of great assistance in making reasonable data projections. In short, I have never really had an idea of what the architects were trying to accomplish there that I feel very comfortable with.
In the course of trying to articulate some of my misgivings about Jean-Pierre Houdin’s ideas about the Great Pyramid having been constructed with the aid of internalized ramps, I find myself drawn back to the troublesome 3rd Dynasty pyramid because it’s been proposed with some frequency that the Giza pyramid may have been built around stepped cores that may be similar to the stepped components of the 3rd Dynasty pyramids of Djoser or of Sneferu’s Meidum pyramid, and trying to determine if what was typical for them might be compatible with Houdin’s ideas about the Great Pyramid as they are continually being depicted.
Offhand, I remain skeptical of Houdin’s proposal, but the exercise involves trying to have some idea of what was intended at Meidum. In the course of this I’ve begun examining photographs of the Meidum pyramid and making traces and overlays. I’ve become more convinced that for the stepped core the intent may indeed have similar to that for Djoser’s pyramid, of steps of equal height, which is a minor breakthrough that may help permit better projections of the original proportions of Sneferu’s Meidum pyramid.
In general, though, I have a lot of catching up to do with the 3rd Dynasty pyramids for having so long ignored them as potentially insurmountable challenges analytically.
It’s here that the subject begins to ostensibly overlap with the subject of the often-mentioned “hypothetical missing pavement layer at Giza”, which is why the preceding remarks, which mostly amount to non-news, serve as preface here.
It’s only been some 3 and a half years ago that I drafted the proposal of the missing pavement layer, which reconciles Carl Munck’s utterly brilliant Great Pyramid model with the current physical reality at Giza. There is a great deal that still isn’t known about it, including how it affects the Giza Layout, which may first require having some understanding of what is being affected.
I can say that recently the first experiment into this matter has been attempted only a few days ago, and successfully.
I don’t what lies ahead in this area, but I certainly encouraged by this.
Specifically, the distance due East-West from the W edge of Cheop’s pyramid to the E edge of Chephren’s that is obtained from combing Petrie’s data with my models of the Giza pyramids is a projected 365.9187465 ft. This looks a great deal like some form of the Solar Year, or possibly the Leap Year.
The Leap Year (~(366 days) is still largely a gray area, and moreover has again been superseded by other concerns, this time by the very recent attempts at identifying how an abbreviated Solar Year of 364 days was accommodated by the same mathematical system already expressing multiple forms of the 365 day year.
One possible identification of this number of approximately 365.9187465 is the “Usk River Number” 365.8052902, which was discovered in Prof. Thom’s data for the Usk River stone circles site. Its importance has been demonstrated on a number of occasions now, although it seems to remain unknown for now how to classify this number – is it an oversized figure for the Solar Year? Is it an undersized figure for the Leap Year? What is its nature exactly?
This may be a rhetorical question at Giza if this nomination doesn’t survive the assessment of the immediate mathematical environment in which it occurs, but to get to the point, if we add the hypothetical missing pavement layer, the number draws compellingly close to the standard, ubiquitous 365 calendar year, the “civil calendar” of the ancient Egyptians.
The history and evolution of the missing pavement proposal is that Munck’s remarkable figures the Great Pyramid, as far as I am able to tell, came about almost by chance. Understandably put off by the discrepancies between some of the different data sources for the pyramids, Munck apparently seized on a passing reference from Ahmed Fakhry to a baseleng of about 754 feet, considerably shorter than the mean of about 755.7 obtained from some of the most harmonious data sources.
It’s rather surprising that Munck didn’t seize upon the general consensus between Petrie, Coles, and Lehner/Goodman for the Great Pyramid’s measures, and yet it’s a very good thing that he didn’t.
Beyond that, other than endless matheamtical evidence for the validity of Munck’s figures, I have little to say about Munck’s departure per se except that it wouldn’t be the first time that the reckless presentation of pyramid data by I.E.S. Edwards or others has thrown a monkey wrench (or spanner, for our friends “across the pond”) into the works. Because of Munck’s acceptance of Edwards as a data source for Mycerinus’ pyramid, I had to revise the Myceronus model from the ground up myself several years ago.
Regarding evidence for the missing pavement, it unfortunately seems to remain circumstantial, even if compelling through its cumulative nature. Overhead views of the current pavement around all three of the major Giza pyramids shows an erratic array of material that is almost begging for an additional “cosmetic” layer to tidy it up.
Remnants of the Great Pyramid’s casing stones in places show signs suggestive of having been protected from weathering by an additional now absent layer. There are also places along the base where unevenness of execution is implied, something else that may call for a cosmetic cover-up with additional, now missing, pavement.
Egyptologist’s view of the Red Pyramid indicate a pavement layer encroaching upon the lowest casing stones exactly as the Giza “missing pavement” model projects having been present there. (This is purported to be according to diagrams by Josef Dorner which I currently do not have in my possession).
Thus far I am of the opinion that this missing pavement would have consisted of prized material perhaps similar if not identical to the material found underneath the Pyramid Temple at the East foot of Cheop’s pyramid, and may have been fitted into the pyramid’s enclosure wall (rather than under it), so that this prized and relatively thin missing layer would have been easily accessible, easily carted off, and thus may not only have been the very first thing to be plundered for material to recycle, but because of this, was also thoroughly picked clean, leaving little to attest to its former presence but the circumstantial evidence cited, unless I’ve underappreciated more possible evidence.
Remnants of black basalt paving from beneath Cheops’ pyramid temple. Photo: Jon Bodsworth.
In the case of Mycerinus’ pyramid with unfinished dressing at the base, it may be very possible that the stage of applying this pavement there was never achieved, since this missing pavement layer is presumed to to have been placed against the finished casing.
The Great Pyramid’s missing pavement would have been a bit over a half a foot thick, and that of Cheop’s pyramid somewhat less, the exact figures being the difference between the “paved” (Munck) and “unpaved” (mine) heights. For the Great Pyramid, that is 481.0325483 ft – 480.3471728 ft = .685375457 ft.
An early breakthrough in this area was the realization that the Great Pyramid (and others) would have metrological and mathematically significant values with or without the hypothetical pavement layer.
Please note that these same considerations may apply to any and all ancient Egyptian pyramids. On this account, there may ultimately be no such thing as an ancient Egyptian pyramid that has singular height and base length measurements.
At any rate, why this is of relevance here is that although I am not necessarily in possession of data for Sneferu’s Meidum pyramid nor Djoser’s pyramid at Saqqara, and although accepting pyramid data from authors like Edwards, Lehner or Rossi is even riskier than accepting candy from strangers (one reason that I do not have finished models of these pyramids), if we look at the data that Lehner presents in The Complete Pyramids, we have
Djoser: base 121 x 109 m, height 60 m
Sneferu: base 144 m, height 92 m
Recalling that Munck’s proportions of the Great Pyramid are height 480.3471728 ft x 2 Pi = perimeter 3018.110298 ft, for Djoser’s pyramid we have
121 + 121 + 109 + 109 = 460 m = 1509.186352 ft = 3018.372703 / 2
Perimeter / height 460 m / 60 m = 7.666666666
For Sneferu’s, 92 m = 3018.372703 / 10 ft
Perimeter height (144 x 4) / 92 = 6.260869565
To my sensibilities, that is about one random coincidence too many, but there is more.
2 x Pi = 6.283185307, which is thought to be the Great Pyramid’s perimeter / height ratio, and which the final perimeter / height ratio of Sneferu’s Meidum pyramid may easily have been also.
Munck’s height for the Great Pyramid divided by 2 Pi = 480.3471728 / (2 Pi = 7.644962696 (compare 7.666666666).
Between the two of them, then, these very speculative heights for these these two 3rd Dynasty pyramids would frame the ratio
Djoser 7.644962696 / Sneferu 6.283185307 = 1.216733603, the value of the Egyptian Remen in “modern” feet.
Thus some of the best circumstantial evidence for Munck’s unorthodox Great Pyramid values, and the missing pavement proposal that supports them, may come from the proportions of other Egyptian pyramids, including even older ones than those at Giza.
This data accuracy reflecting the original intent here would also indicate that not even Egyptologists can spoil all of the data, all of the time.
By the way, if anyone spotted it in those figures, you are correct – that is one of many important things that the Great Pyramid’s height according to Munck means:
480.3471728 / 2 Pi / 2 Pi = 12.16733603, the Remen in feet
I’m probably not up to task of trying to track down this missing layer of pavement, nor do I need another thing to juggle at the moment, but obviously the logical place to begin a search might be some of the the oldest Egyptian structures to be built from pillaged material taken from the Giza plateau.
For the moment, I thought I would attempt a fresh explanation of why Munck’s Great Pyramid seems to be a foot shorter than everyone else’s, and why it may matter to both the study of, and the story of, the 4th Dyansty pyramids at Giza, and the 3rd Dynasty pyramids at Meidum and Saqqara.
These numbers may still hold the key to understanding whether what we see at Meidum and Dahshur is the result of accident, or the result of careful and organized planning.
–Luke Piwalker
Luke Piwalker 
