Luke Piwalker

The Granite Box in the Pyramid at Lahun (Part 1)

I am greatly indebted to DUNE at GHMB whose fascinating work on this object got me intrigued with it again. (I am referring to it herein as a “granite box” although the orthodox view is of course that it is a sarcophagus). For readers wanting more background on the pyramid of Sesostris II (Senusret II), Keith Hamilton’s Layman’s Guide to the Illahun pyramid is highly recommended.

I have posted previously about various aspects of the pyramid itself.

Section from WMF Petrie’s plan of the surprisingly elaborate internal structure of the Lahun (Illahun, El-Lahun) pyramid, showing the location of the granite box within the “granite sepulchre” chamber.

I don’t know how much optimism I have that I can solve the riddle of the box’s original design specifications – I’ve become accustomed to having difficulty solving the original proportions of any ancient Egyptian coffers. It’s as if the mathematics involved is so “Royal” as to nearly defy analysis sometimes – as if their original designs may be so brilliant as to nearly defy comprehension.

All the same, I can take some encouragement from various initial observations about the box, and from the idea that the box is not unlike the King’s Chamber in the Great Pyramid – deceptively simply at first glace.

Above: The “sepulchre chamber” containing the granite box. Note how the box is taller toward one end (the North end, to the right in the photo. Below: the sarcophagus chamber in Mycerinus’ pyramid at Giza, which is frequently compared to the Lahun pyramid’s sepulchre chamber on account of the rounded ceilings they have in common .

Above: the raw data from WMF Petrie for the dimensions of the Granite box. Below: diagram labelled with Petrie’s data and some extrapolations of the data.

Much of the data seems to simply be in units of the two most likely ancient Egyptian units to encounter, the Royal Cubit and the Remen. However it appears that that they managed include the Megalithic Yard, Megalithic Foot, and quite possibly other units that may be hiding in the unidentified values of 8.843, 0.4980833333, 0.75333333, and 1.07 ft. (It’s worth noting that 1.07 feet is close to the 1.067438159 ft Hashimi Cubit).

The particular suspected expression in Megalithic Feet is something of a surprise. This is something I consider more likely to be encountered in the ancient Americas, where the number may have been favored because of some of it’s astronomical properties. Mathematically, 1.96207628 is ((1 / 1.622311470) / Pi) x 10.

The value of 97.165 inches, labelled here as 6.666666666 Remens, is intriguing. It is likely to be exactly that: 6.66666666 x 1.216733603 = 8.111557353 ft = 16.22311470 / 2 ft. Some doubt remains because it might also be 16.18829140 / 2 = 8.091414570 = 97.12974840 inches.

(6.666666666 Remens is not a rational value in the Inductive Metrology sense, but for now it will do for purposes of discusssion).

We have found the value of 97.12974840 feet at Stonehenge as the inner lintel circle diameter, but only long after finding 80 Remens = 97.33868822 ft as the inner sarsen circle diameter.

16.22311470 comes first, so to speak. I frequently tell people that 1.622311470 and 1.177245771 are two of the most important things to try to build into every pyramid somehow, and the granite box appears to be no exception – note that from the raw data, the outer length (measured without, or below, the lip) divided by the inner length = 97.165 in / 82.495 in = 1.177828959, very likely to mean 1.177245771.

They have seemingly chosen the proportions very carefully so that this hugely important number appears as a ratio in the most straightforward manner possible.

It’s not entirely certain yet which form of the Megalithic Yard they used here. (In my experience, it’s best to start with 2.720174976, followed by 2.719256444, in investigating such matters).

Curiously, I’m not entirely certain which form of the Remen they used for the North end height, either. Normally we expect a certain amount of consistency with a subject when it comes to forms of a particular unit, but I’m seeing some possible schemes that may make the Short Remen out of the height value, whereas the “6.666666666” Remens of the outer length is almost certainly the Long Remen of 1.216733603.

Possibly, if the Remen used for the North end was the Long Remen of 1.216733603 ft, the Megalithic Yard used at the South end was probably 2.720174976 ft; if the Remen used for the North end was the Short Remen of 1.2158542204 ft, the Megalithic Yard used at the South end was probably 2.719256444.

There may be further metrological clues provided by some of the measures appearing to be simple fractions of others.

The 2.21075 figure is somewhat mysterious – not for lacking good candidates, but for lack of a decisive scheme to which the number belongs. Furthermore, it may repeat itself.

One candidate is 2 Indus Feet (2 Long Indus Feet = 2.201849257 ft); another is 2.219055999, and there is also 2.210485321 ft, which is the reciprocal of 1 / 2.210485321 = 4523.893421 / 10^n. One or all of these might be featured here depending on the actual specifics of how the proposed parts work together interactively.

452.3893421 ft is what I have traditionally given as the height of the Great Pyramid from the pavement with the apex section missing. In Royal Cubits, it is 1.622311470^2 x 10^n. That’s one of the ways they seem to have smuggled this number that all pyramids should contain, into the Great Pyramid – in spite of a rather busy agenda for what the design should be able to communicate.

So there is sort of an overview of some initial impressions. At least one more part should follow wherein we can take a closer look at some of what has been proposed. I emphasize the comparison to the King’s Chamber, of seeing something that may be very deceptively simple-looking, because the parts are simple, but how they have been chosen and combined may be nothing short of amazing.

–Luke Piwalker

Some Initial Impressions of the Pyramid of Unas

Not surprisingly, I am unable to find prior work on Unas’ pyramid, since the subject is fraught with a fair amount of uncertainty, beginning with the raw data itself. Even if the raw data can be taken seriously, however, there is still room for uncertainty about the matter.

A number of Egyptian pyramids may remain unsolved, or even unattempted, because eventually what happens is surprising diversity.

Just as is the case with the Royal Cubit, eventually the overall body of Egyptological data becomes voluminous enough that we can begin to see the unlikelihood of everything having been measured in Royal Cubits only, so too does the body of architectural data become voluminous enough on the whole that is may both contraindicate the use of sekeds in actual pyramid design, and rule out any convenient “rule of thumb” for pyramid perimeter / height ratios.

As such, it becomes harder to identify authentic data when correct or incorrect data, some of the raw perimeter / height ratios are just plain strange, even with a considerable amount of experience to guide an interpretive effort.

If I give the raw data I have for Unas’ pyramid the benefit of a doubt that is may indeed be another Egyptian pyramid with a simple number (in this case, 100) Royal Cubits in the base, we still seem to be looking at something curious.

One thing that is unusual about what emerges tentatively from the data, is that the Half Venus Cycle (Mayan Calandar Round) very much seems to be on display. I think this is an idea that may difficulty catching on for perhaps both lack of scholarly support, and the desire among researchers to have as much scholarly support as possible, but the mathematics of calendars is after all universal.

I have yet to be able to overturn the idea that the height of the pyramid was 120 Megalithic Feet. An homage of this sort, or an additional one, advertising the Megalithic Foot / Alternate Pi has been expected for some time, and this choice of a height value has some remarkable consequences.

However, the actual version of the Calendar Round chosen for representation, and the consequences of that choice, seem more or less uncertain.

For reference, such a pyramid feature may not be entirely without precedent. From Petrie’s raw data, the upper part of the Bent Pyramid at Dahshur also seems to be expressing some form of the Calendar Round.

Note the height of the Bent Pyramid’s upper section from Petrie’s own data. 2277 inches = 189.75 feet, very close to the canonical Calendar Round 18980 / 100 or one of numerous possible useful approximations of it, at least some of which we can find license for from Mayan calendar math itself.

One difficulty with the Calendar Round, being it is near to the (square root of 360) x 10^n, is that there are forward and “backhanded” forms of it

To use the B value for the Half Venus Cycle / Calendar Round to illustrate

HVC B 18997.72194 = (360 x (10^n) / 189.4964044

Such backhanded forms have been referred to before as “Builder figures” because we can build the forward forms from 360 and the “Builders”, and such figures appear to have been included in artifacts such as the very calendar oriented Aztec Sun Stone.

At the moment, I’ve chosen three candidate sets for the proportions of Unas’ pyramid, but I still don’t understand clearly the “Modus Operandi” (plural) at work.

I’ve shown in the past how easy it is to find three different forms of the Calendar Round in the Great Pyramid using onlywhat we are given by the pyramid

However, Unas’ pyramid may have more ideas.

The general trend in projected data sets, particularly the more favorable ones, is

Base in feet = some form of the Calendar Round / 100; height = 200 Megalithic Feet; vertical edge = ~194.8181821 ft, and apothem = ~Faiyum Oasis Wonder Number 170.2535130

There are two promising versions that use the A and B Calendar Round / HVC values for the base.

The third promising version is quite surprising. For the base value, it employs a fourth form of the Calendar Round / HVC that has been projected systematically but never detected in ancient architecture before that I am aware of.

The D value for the HVC is 2 x (Pi^8) = 189770.06203, representing the canonical 18980 day Calendar Round.

One remarkable thing about this model is that it may have the most pleasing diagonal value

189.77006203 x sqrt 2 = diagonal = 134.1880925 x 2 = ~1.676727943 x 80 = 134.1382354 to an accuracy of 134.1382354 /134.1880925 = an acceptable .99962845 = ~99.96%

Personally, I am not eager to have anything except the core set of planetary values sets A-C validated by the ancients, it threatens to make all our headaches from trying to keep up with ancient math warriors 33% more severe, but there is a special reason that this third proposal stands out.

If we square the projected vertical edge length of 194.8181821 ft (which by the way would share an unidentified fundamental unit of measure with Stonehenge’s outer sarsen circle and with the Great Pyramid’s height from the base level) we get 194.8181821^2 = 37954.12406 which would be the D form of the Full Venus Cycle

37954.12406 / 2 = 18977.06203

So did they repeat this curious forth value in both the base, and the vertical edge via square root, for emphasis and reassurance as to the deliberateness of such a gesture, or is the pyramid perhaps really trying to somehow express a more diverse set of Calendar Round values than that?

Why I am writing this, even without having further insights into that all-important question, is because that whatever the exact specifics of which versions of the Calendar Round were incorporated, it continues to seem very likely that the Faiyum Oasis Wonder Number was used here.

Some readers might also remember that it was proposed that the Faiyum Oasis Wonder Number came into prominencebecause of its direct relationship to the Calendar Round, in general reference to the A value.

At any rate, what it looks like is that this Faiyum Number, which came into prominence in the Faiyum region in the architecture of the 12th Dynasty, was already recognized and utilized at Saqqara in architecture attributed to Egypt’s 6th Dynasty, implying that it had already reached a fully realized state no later than the Sixth Dynasty.

As recently I had been exploring the data on Khendjer’s pyramid, it might be of interest that if my calculations are correct, the slope of Khendjer’s pyramid without its capstone comes within reasonable tolerances to 1/2 of the RMA (“Real Mayan Annoyance”)

That is, the pyramid base beneath the slope without capstone probably being 83.65644028 ft = 40 Sacred Cubits of 2.091411007 ft; 2.091411007 ft = Royal Cubit 1.718873385 x Remen 1.216733603, and the height without the capstone appears to be probably 120 feet Imperial, thus

sqrt ((83.65644028^2) + (120^2)) = 146.2819196 ft = ~146.3221164 = (29.26442328 / 2) x 10, 2.926442328 being the so-called “Real Mayan Annoyance” (annoying because it isn’t 2.920160646, and at least as Egyptian as Mayan).

The Faiyum Wonder Number (FWN) being 1.702535130, perhaps it’s slightly interesting that

RMA 29.26442328 / FWN 1.702535130 = 17.18873388 = Royal Cubit in feet x 10, exactly.

That’s the very same good old Morton Royal Cubit that is indicated to us by the Great Pyramid because 17.18873388 is the ratio between the whole pyramid and the missing part (missing apex section).

–Luke Piwalker

Another Way of Relating Ancient Units of Measure to Each Other?

I had previous opportunities to spot this – I believe it was either Richard or Robin Heath who commented that if you subtract 1 Foot Imperial from 1 Megalithic Yard, you get 1 Royal Cubit. It doesn’t work out exactly, but it’s too exact to simply fade away.

I have no pretensions here of having just uncovered a way of relating different ancient units of measurement that is going to exceed last year’s discovery of their relationship through the geometry of the circle, nor will the original approximate relationships of ancient units of measure through squares and rectangles ever exceed their relationships through circular geometry.

However, the formulas relating to squares and rectangles are hardly invalid, and they can be an often have been adapated into precise and meaningful formulas.

A great example of this is how the relationship between ideal Royal Cubit and ideal Remen, while not precisely sqrt 2, thus involves an alternate form of sqrt 2 that is based on the Megalithic Foot, precisely.

That said, what I have to offer are observations on the addition and subtraction of various units to or from one another.

I may have missed Hearth’s cue involving this phenomenon because at the time I learned of it and experimented with it, my palette of metrological units was a little too limited to recognize it. At that point, I probably had yet to accept the Megalithic Foot 1.177245771 or Ancient Egyptian Mystery Unit 1.676727943 ft as metrological values. The Pied du Roi/Hashimi Cubit/Egyptian Royal Foot values were likely not fully accepted at the time, either.

So here are a few examples of that I’m talking about.

Royal Cubit 1.718873385 – Egyptian Mystery Unit 1.676727943 = 0.421454420; 1 Palestinian Cubit 2.107038476 / 50 = 0.4214076952
Egyptian Mystery Unit 1.676727943 – Hashimi Cubit 1.067438159 = 0.609289784 = .5 x 1.218579568; “Thoth Remen” = 1.218469680
Palestinian Cubit 2.107038476 – Remen 1.216733603 = .890304873 = 2 / 2.246424014 (Petrie Stonehenge UNit 224.8373808 inches)
Long Meter 3.289868134 – Hashimi Cubit 1.067438159 = 5 / 2.24978967; Venus Orbital Period C = 224.913272 (days)
Palestinian Cubit 2.107038476 + Megalithic Foot 1.177245771 = 3.284284247; “Radian Squared Meter” = 57.29577951^2 / 1000 = 3.282806350
“Radian Squared Meter” 3.282806350 – Megalithic Foot 1.177245771 = 2.105560579; Shorter Palestinian Cubit = 2.105515606
Palestinian Cubit 2.107038476 – Megalithic Foot 1.177245771 = .929792705; sqrt 8640 = (1/225 Sacred Cubit) x 10^n = .9295160031
Petrie Stonehenge Unit 18.73644840 ft – Megalithic Yard 2.720174976 = 16.01627342; aside from 16.000000 Imperial, 15 Hashimi Cubits = 16.01157239
Petrie Stonehenge Unit 18.73644840 ft + Hashimi Cubit 1.067438159 = 19.80388656; 18 Short Indus Feet = 19.8014214
Megalithic Yard 2.720174976 – Hashimi Cubit 1.067438159 = 1.652736817; 1.5 Long Indus Feet = 1.651311942
Megalithic Yard 2.720174976 – Remen 1.216733603 = 1.503441373, which may be sufficiently close to the figures discussed in the previous post concerning the pyramid of Khendjer and the pyramidion of Teti.
Megalithic Yard 2.720174976 + Remen 1.216733603 = 3.936908579 = (3.280757140 / 12) x 10; Modern Meter = 3.280839895; suggested ancient “shaved” meter = 3.280433687
Megalithic Yard 2.720174976 + Megalithic Foot 1.177245771 = 3.897420747, which appears to be in the Stonehenge Sarsen Circle unit (51.9515151 / 1.333333333 = 3.89636363)

There’s another interesting thing to come out of this as well:

Palestinian Cubit 2.107038476 – Royal Cubit 1.718873385 = 3.881650910 / 10, which seems uncannily like the 38.81346810 astronomical and geodetic figure discovered at Tikal and taken from Teobert Maler’s data.

Carl Munck’s drawing of Tikal Temple I labelled with Teobert Maler’s data.

It has recently been noted that 38.81346810 has metrological value. It appears to be in the Egyptian Mystery Unit of 1.676727943 ft: 1676.747941 / 432 = 3.881346810.

So we are just getting started with relating ancient units of measure to each other through addition and subtraction, but the number of “hits” so far is remarkable.

So what are we to think of this amazing bundle of units I am working with, that relate though one another through squares and rectangles, AND through circular geometry, AND through multiplication and division, AND though addition and subtraction?

What are the odds against such an incredible system having arisen by accident, or without its creators knowing what they had and what they were doing with it?

–Luke Piwalker

Khendjer’s Pyramid

I don’t believe I’ve ever posted before on Khenjer’s Pyramid – and probably not due to some lingering uncertainty about the matter. However, having tried to look into the matter a little further now, I believe I have may have found some interesting things.

Khendjer’s Pyramid (at Saqqara)

The first thing I should probably do is have a look at Keith Hamilton’s Layman’s Guide to the Khendjer Pyramid.

The Pyramid of Khendjer and pyramidion (capstone) from Mark Lehner, “The Complete Pyramids”.

I have already been looking at some data in the meantime however. Basically, Lehner and Verner give the same unattributed proportions for Khendjer’s pyramid, which apparently can be traced back to Gustave Jequier in Deux pyramides du moyen empire (1932).

The French Wikipedia page listing Egyptian pyramids also gives a base length, also unattributed, to the adjacent smaller pyramid, of 25,5 m. I am not certain if Jequier is the source for this figure; Dieter Arnold is also mentioned in the bibliography for the Wikipedia page in English on Khendjer’s Pyramid
https://en.wikipedia.org/wiki/Pyramid_of_Khendjer

What I have done this time around apparently is to try begin looking more closely at some alternate possibilities.

At least five different sets of possibilities can be generated

The first set is interesting, and I tended to think the figures were correct. Not only is the perimeter/height ratio an homage to the Venus Orbital Period, but the apothem tries to appear to be one also since 149.8915869^2 = 224.6748781 may be a valid if diverse way of writing the Venus Orbital Period.

Additionally the listed height of 122.3194031 ft is 1/5th of the Great Pyramid’s slope length (apothem), which is itself twice the inner sarsen circle perimeter of Stonehenge.

Aside from the curious vertical edge figure, it does have numerous earmarks of a sound proposal, yet these figures have now been challenged by numerous other possible proposals.

We may ultimately be able to get a better sense of realism about Jequier’s figures by looking at the archaeological environment, i.e., other pyramids at Saqqara and so forth.

Indeed, one of the things that has come to light during this round of attempting to understand the design of Khendjer’s pyramid is there may be some notable parallels between Khendjer’s pyramid and Teti’s pyramid, which is also at Saqqara,even though Teti’s pyramid is dated to the Sixth Dynasty and Khendjer’s to the Thirteenth Dynasty.

Several years ago, I developed this partial model of Teti’s pyramidion based on the available data, which was quite convincing considering it seems to describe a pyramidion base measuring 1 Remen by 1 Royal Cubit.

Teti’s Pyramidion

Length 1.718873385 Royal Cubit
Width 1.216733603 Remen
Diagonal 2.105515605 Palestinian Cubit (Shorter form)
Apothem A (on long side) 1.62231147 Assyrian Cubit
Apothem B (on short side) 1.731717175
1.509 = ? = raw figure for height

What they have done here is seemingly use 1.731717175 as a false square root of 3 and place it in an important and necessary place where a Royal Cubit will not fit, illustrating for us that 1.731717175 / 1.622311470 = 1.067438159.

It’s quite an interesting and compelling model, and seems to have remarkable focus on metrology, revealing the most straightfoward expressions of the Remen, the Royal Cubit, the Palestinian Cubit, the Assyrian Cubit, and by way of ratio, the Hashimi Cubit / Egyptian Royal Foot – almost a sort of “metrological Rosetta Stone”.

More realistic projections of the uncertain height of Teti’s pyramidion may come very close to (1/100th of) the projected apothem length for Khendjer’s pyramid. Hence Khendjer’s pyramid may directly reference both the height and short-side apothem of Teti’s pyramidion, suggesting possible strong observance of Saqqara’s Sixth Dynasty past during Thirteenth Dynasty architectural design.

Also, Hamilton notes data on the enclosure walls, which might be useful further along – generally I am not that far with this study yet.

Returning to the data, then

For the second set, at first I was skeptical of this because 200 / 123.0162633 = 1.625801294, which is data from the Great Pyramid’s apex section, but presumably this figure would come third after 200 / 1.622311470 or 200 / 1.618829140.

However, this gesture has the interesting consequences of generating 5.589093147, thought to be the primary representation of “56” at the 56-holded Stonehenge Aubrey Circle. It was found by fellow researcher Mercurial at GHMB and myself that numbers close to 56 seem to be rather useful for linking components of calendar cycles.

(https://grahamhancock.com/phorum/read.php?1,1233299,1233882#msg-1233882 and other posts in thread).

For this projection, the apothem is plausibly 150 feet “Imperial” and the vertical edge is an important figure since the raw projection 172.9324416 ft seems acceptably close to 172.9249823

It would be a “geodetic modelling cubit” in that it allows modelling the earth at a ratio of feet:miles, i.e, 172.9249823 x 144 = 24901.19742, a high accuracy approximation of the number of miles in Earth’s equatorial circumference.

This value appears in the baselength for Mycerinus’ pyramid in my model, revised from Munck and based on Petrie and Dash rather than I.E.S. Edwards, which Munck based his Mycerinus model on.

In deference to Morton’s Royal Cubit of 1.718873385, we do not need to classify 1.729249823 as a Royal Cubit; rather this value of 172.9249823 can be seen as 162 Hashimi Cubits or perhaps more directly as 150 Egyptian Royal Feet. (Twice this value in Long Indus Feet is Pi x 10^n).

The third set is based on 200 / 1.618829140 = 123.5460834. The ability to express the best and most certain form of the Eclipse Year.

For the fourth set, the apothem can’t quite pass for 150 Imperial accuracy-wise (.9993) but the vertical edge may be able to pass for 172.9249823 and the perimeter/height (P/H) ratio may be the second most likely approximation of 56 to be involved with the Stonehenge Aubrey Circle. The origin of the height may be essentially Egyptian Royal Foot x Hashimi Cubit (Pied du Roi) but it might be doing little more than getting caught in a slight mismatch in this sector of the numbers that might be best avoided.

The 200 / x gesture does generate a known number with 123.0578165, but it may be at least 4th in usefulness behind the number obtained from the Great Pyramid’s missing apex section. To the best of my knowledge, it has never been found in ancient architecture before, which may indicate that it is overshadowed by other similar but more important numbers, and with good reason.

I don’t want to be hasty as there is so much here to consider, but offhand I think I would place the highest confidence in either the third or fifth set of projected figures.

For the fifth set of figures, the merits include that it is “crowned” with a height value that is, as I’m sure many know by now, the second most powerful data retrieval tool known. It has a pleasing and significant P/H ratio, one with an established history reaching back to Munck’s own work, a value that has been shown lately to be in putative Egyptian Sacred Cubits.

What also seems meritous about this is that for the apothem and vertical edges seem to reflect the design of Teti’s pyramid.

If take the Edge/Apothem ratio to be, rather than 1.152, the preferred figure of 1.152 x 1.000723277 = 1.152833215, then

173.1717171 / 1.152833215 = 150.2140248 = 150.2813756 to .9995551835 accuracy.

If the pieces should seem to be poorly interactive, it may be because these figures were put there as “fodder” or “tinder” for the height value to work its powerful magic unlocking various data from them.

So the matter isn’t decided, but a more extensive effort than previously may have been made, and that is the state of the projections at this hour.

The Pyramidion and Subsidiary Pyramid

The data we have from Corinna Rossi, Architecture and Mathematics in Ancient Egypt, gives us for the base length of the pyramidion, 141 cm = 4.625984252 ft, also giving the same value for the vertical edge. Thus we have a pyramidal structure with height approx 3.271064835 ft (3.270127141 ft?), diagonal of approximately 4.625984252 x sqrt 2 = 6.542129669 ft = ~6.540254281

Perhaps the two most likely things for the base length to mean would be (sqrt 2160) / 10 = 4.647580015 and (2.720174976 / 1.177245771) x 2 = 4.621252491

It may actually be difficult to choose between one and the other. The first is a very striking, very straightforward match for the suspected height figure, while the second is part of a remarkable data stream that can be mined with the suspected height figure.

We might wish to place emphasis on this being a dramatic example of mismatched pyramid and pyramidion angles. which may have been something of the norm.

When relating the pyramidion to the pyramid, then, rather than subtracting the pyramidion’s height from the pyramid’s total height, what we want to do is determine the minimum height at which the pyramid is able to fit completely onto the pyramid’s summit.

Thus, 171.8873385 – 4.625984252 = 167.2613542 ft; that is, the edge of the pyramidion sits inward horizontally 167.2613542 ft from the edge of the base – and 167.2613542 resembles a fairly well known figure in Sacred Cubits –
and thus we will use the height/half base ratio from the projection, 123.28088888 / (171.8873385 / 2) = 1.434438278, to determine the height from the edge of the base at which we first encounter the pyramidion horizontally from the edge

(167.2613542 / 2) x 1.434438278 = 119.6630333 = 120 to accuracy .9971919

167.2613542 resembles the figure in Sacred Cubits, 167.3128806 ft = 80 Sacred Cubits = 80 x 2.091411007 ft, and

(167.3128806 / 2) x 1.434438278 = 120 exactly, while

167.3128806 + 4.647580015 = 171.960460615 = 171.8873385 to 0.999574773673
167.3128806 + 4.621252491 = 171.934133091 = 171.8873385 to 0.999727834199

So we see that either base length for the pyramidion combines with 80 Sacred Cubit to successfully approximate 100 Royal Cubits in pyramid base, to .9995 or higher.

We may also want to note that if the projected height of the pyramid is 123.28088888 ft and the height without pyramidion is 120 feet, the difference is 123.28088888 – 120 = 3.280888842, a remarkable approximation of the contemporary meter of 3.280839895.

One other thing that I would like to draw attention to here is simply that 167.3128806 / 2 = 83.56644030.

I could mention that 16731.28806 came from Munck’s own research, I would mention that 167.3128806 x 3.333333333 = 5.577096019 x 10^n (see perimeter / height ratio for total pyramid)…

Mainly, concerning the subsidiary pyramid, wherever Wiki.Fr got the information, it is remarkable that the base length given by them is 25,5 m.

25.5 m = 83.66141732 ft. Again 40 Sacred Cubits would be 40 x 2.091411007 = 83.656444028 ft, which we also found in the main pyramid, not that Egyptology is likely trying to think in Sacred Cubits.

Thus, while at this hour we may still lack a definitive, exhaustive interpretation, we may have made some very meaningful observations about the data and its possible quality, making Khendjer’s pyramid seem as if it is among the ancient Egyptian riddles which can be solved.

Cheers!

–Luke Piwalker

I Missed Mexico

While most of us including me seemed to think the El Castillo pyramid at Chichen Itza had 91 steps per staircase, I recently posted about the diagram from Maler showing more than that, and the text from Maler indicating 96 steps per staircase.

So much for 4 staircases x 91 steps = 364 and 9 terraces x 91 steps = 819, I guess which must be a concoction of government officials and archaeologists attempting to pander to tourists?

http://everythingcozumel.com/miscellene … -delusion/

So what is the meaning of 96? I’m not very sure yet, but we may wish to observe that if using our customary numbers in this work, 96 links the Earth Year to the Venus Cycle, connecting what may be the two most important numbers in the calendar.

The figure may be variable, and it’s an interesting case of that. 96 is a valid number which unlocks the B version of the Venus Cycle from the same form of the Solar Year (3600 / Pi^2 days) that we find indicated in Maler’s data for the base proportions, but we will also need to interpret is as 96 x 1.000723277 to also unlock the A Version of the Venus Cycle. What is thus proposed is very similar to what is proposed for the Aztec Sun Stone, which is able to portray both the A and B versions of the Solar Year and Half Venus Cycle due to its variable height (thickness) parameter.

In penance for helping to spread the “91 steps” figure, I decide to have another look at Marcello Raineri’s data projections on the El Tajin calendar pyramid. His base length matches that of Grijalba, whose data Raineri may have used to calibrate his efforts, but only a singular figure is given by Rainieri when the footprint shown by Grijabla is more intricate and thoughtful than that.

Still. I might just be beginning to understand some of the measures given by Raineri, who expresses the measures in “ma units” of .499 m, which is by rights no more a mere millimeter away from Raineri being yet another researcher to advocate for ancient American metric units.

Once again I’m gratified at what I’m finding in Raineri’s data

https://www.academia.edu/23492562/A_GEO … E_CALENDAR

Something that I think particularly interest even for as little overall progress as I’ve made so far, is as follows…

A few years back I worked on the crude numbers in El Tajin, particularly the number of features on the staircases. This seems to be a direct extension of what we can find at Tikal. It’s hard for me to make sense of sticking great big blocks in the middle of Temple stairs, but the mathematical parallels between a large block in the middle of the Temple stairs of one of the Tikal pyramids, and the five large inclusions with three niches each in them at El Tajin.

Thus far such inclusions seem to be used as a symbol to indicate the use of a related square root. At Tikal, I used my best effort at photogrammetry on a photograph by Edwin Shook to supplement George Andrew’s missing data point for the block, to determine that that block imitates the Temple door width of 1 Squared Munck Megalithic Yard = 7.396853331 ft to show us that

7.396853331 / (Radian / 10 = 5.729577951 = 1.2909944449 = 1 / (sqrt 60)

1.2909944449 or it’s reciprocal form 1 / (sqrt 60) is THE most powerful data recovery tool ever discovered, which also has shown up in at least two of the other sites selected by Raineri for his paper.

At Tajin, we have the option of reading 5 inclusions of 3 niches as sqrt 5/sqrt 3 = 1.2909444449

Or taking the square root of the total 15 niches as (sqrt 15 = sqrt 60) / 2 – and after all, sqrt 15 is 1/2 of sqrt 60. A bit resplendent of Stonehenge in that way, where sqrt 15 and sqrt 60 are eminently useful and Munck thought them specifically indicated by the unusual displays of 60 stones in the circle and 15 in the trilithon “horseshoe”.

What Raineri’s data says to us is that on this very same staircase, the ratio between the total width of the stairs including staircase plus “side rails, divided by just the width of the stairs = 19.5 / 13 = 15 / 10, and the ratio between the total width of the stairs divided by just the width of the side rails = 19.5 / 3.25 = 60 / 10

What I suspect is that the total width of the stairs, 19.5 ma units = 9.7305 m = 31.92421269, indicates the number 32 x 1.000723277 = 32.02314486 (this is 1/3 of the 96 x 1.000723277 value I am trying to make out of the number of stairs at El Castillo after revisiting Maler).

32.02314486 appears to be a very productive number to combine with sqrt 15 or sqrt 60 or 1 / sqrt 60, forming a series with a variety of calendar data in it.

At the level of one of the terraces, the ratio between that terrace and the next is 53 / 45 = 1.1777777777, which is quite likely to mean the Megalithic Foot value 1.177245771

That is about all I have worked out so far this round, except that the designers may have set up one or two series that may give the same dual geodetic effect that we see at Tikal’s temples as may have first been noticed by Carl Munck.

Munck’s drawing of Tikal Temple I showing the 24.901 ft value from Maler. Earth circumference in miles = ~24901.55. This measurement was corroborated by George F. Andrews in his field work gathering architectural data at Tikal.

These ancient American architects seem quite good at putting their best foot forward before they get too crazy with their math.

–Luke Piwalker

What the “Ancient Egyptian Mystery Unit” Might Be… Maybe…

WHAT “LSR” MAY BE

To be honest, I still can’t rule out that the “Ancient Egyptian Mystery Unit” 1.676727943 may be a variant Sacred Cubit of some kind. Even though it apparently failed to show up even in an elaborate John Neal style display of unit variations, we can not only build the standard Sacred Cubit 2.091411007 from standard Remen x Standard Royal Cubit, but we can build other candidate Sacred Cubit figures from other less-used forms of Remen and Royal Cubit, including one that makes a Sacred Cubit value of 1.676727943

Having hopefully advanced somewhat the case for the Thoth Remen in the preceding posts,

Thoth Remen 1.218469679 ft x Long Royal Cubit (1.718873385 x 1.000723277 ft) = 2.095909929 / 125 = 1.676727943

We can also construct another Sacred Cubit of 2.094395102 ft = 2/3 of Pi, as

Thoth Remen 1.218469679 ft x Standard Royal Cubit 1.718873385 ft

Maybe soon it will be time to ask what else could it be?

-Luke Piwalker

About the El Castillo Pyramid at Chichen Itza

It continues to bother me that there seems to be an unsolved mystery about the El Castillo pyramid at Chichen Itza, which is how many steps did it originally have and how many steps does it have now?

A few years ago when I returned to this work, I predicated a great deal of my conviction that what pyramidal (and temple) architecture really wanted to talk about was calendars – the 364 steps of the El Castillo Pyramid (4 staircases x 91 steps) and the 365 niches of the Pyramid of Niches at El Tajin in Mexico were the very foundation of the exploration to follow leading up to the present day.

It’s too late now of course, the proverbial cat is out of the proverbial bag, but this foundation may have been partly based on false assumptions about El Castillo.

The article “Shadow on the Stairs: A Story of Mass Delusion” by Ric Hajovsky delves into the history of the El Castillo pyramid as well as the practice of inventive restoration in archaeology, often to apparently cater to tourist’s expectations.

Curiously, when I first read it, I felt contented that if 91 weren’t were the original number of stairs per staircase, we would know about it, because it was my understanding that not all sides of the pyramid have been restored.

Lately, it continues to trouble me that 91 stairs per stairway is in apparent contrast to Teobert Maler’s study of El Castillo, where I counted the stairs on the diagram and obtained more than 91.

(I’d even decided that, based on this example, Maler hadn’t been accurately depicting the number of stairs on the structures, which was not only seemingly rather presumptuous, but may have been a big mistake on my part).

Still, it’s been difficult to try to corroborate Maler’s drawings as to whether the number of steps are drawn accurately, since apparently this is somehow rather rare data.

What has prompted this message however is that I went back to Maler’s own text and found a verbal description. From Monumenta Americana, Vol 4, translated by Google

Thus Maler has drawn more than 91 steps and has stated more than 91 steps.

The figure 91 is compelling, because not only do we have 91 x 4 = 364, but El Castillo shows nine terraces, and 9 x 91 = 819, the mysterious but important Mayan Calendar number — but is 91 stairs nonetheless an invention of modern archaeology and restoration?

Likewise, calendar significance is assigned to the number of panels on the terraces – but are these too just modern inventions, more of “the government’s idea of what the ruins should look like”?

As reported previously, however, Maler’s measurements taken prior to restorative work do clearly suggest a “calendar pyramid” in a very real sense, including the ingenious astronomical and mathematical symmetry of the stated base proportions wherein 6 times Pi is used to indicate the square root of the Lunar (Leap) Year, and 10 x (6 divided by Pi) is used to indicate the square root of the Solar Year.

It’s just that I think El Castillo still needs more careful sorting out as to which calendrical features may be original, and which may not.

–Luke Piwalker

Updated List of Metrological Unit Families

I think the revised list enclosed should represent the current state of the art. Offhand I’m not expecting much else in the way of new developments.

‘m rather pleased about a few things, including what I feel is progress with ancient meters. I’ve been looking at those possible ancient meter figures for just under 20 years now and have never had the confidence in them before to present them as proposals, but I think a better overview of ancient metrology and thinking up some better criteria have helped.

Certainly the merit recently afforded a putative ancient meter of 3.289868134 ((1/3) x Pi^2) feet as the probably primary unit value on account of its striking exponential utility, which exceeds that of many known and established units, must be well placed?

1. MEGALITHIC FOOT FAMILY (see Harris-Stockdale Megalithic Foot or “HSMF”)
Megalithic Foot 1.177245771 ft
Indus Foot 1.100874628 ((360^2 / 1000) / 1.177245771)
Pole / Rod 16.51311941 ft (1944 / 1.177245771 / 10)
Alternate Megalithic Foot 1.179778193 ft ((100/72) / 1.177245771)
Megalithic Yard 2.718208958 ft (32 / 1.177245771) (dimeteral unit of circumferential unit of 1.067438159)
Lintel (Circle) Megalithic Yard 2.725105951 ft (1.177245771 x (432 / 100))
Nippur Cubit (speculative) 1.695233910 ft (1.177245771 x (144 / 100)
Nippur Cubit (speculative) 1.698880598 ft (2 / 1.177245771)
Long Royal Cubit (1.718873385 x 1.000723277) = 1.720116607 ft (2025 / 1.177245771 / 10^n)
Possible Ubaid Cubit of 2.354491542 ft (2 x 1.177245771) and/or 2.359556387 ft (1.179778193 x 2)

2. EGYPTIAN LONG REMEN FAMILY (see also Algernon Berriman Historical Metrology for Remen fraction relationships)
Remen 1.216733703 ft
Greek Foot 1.013944669 ft (1.216733603 x 10/12)
Squared Munck Megalithic Yard (9 / 1.216733603)
Assyrian Cubit 1.622311470 ft (1.216733603 / .75)
Egyptian Foot / Roman Foot 0.973386882 ft (1.216733603 x .80)
Roman Pace 2.433467205 ft = Double Remen = 1.216733603 x 2
“Short” Palestinian Cubit 2.102515665 ft (1.216733603 x (1728/1000)) (rare?)

3. EGYPTIAN SHORT REMEN FAMILY
Short Remen 1.215854204 ft (12 / (Pi^2))
Thoth Remen 1.218469679 ft ((1.234567901 x (Pi^2)) / 10) = ((Pi^2) / 81) x 10
Short Greek Foot 1.013211836 (10 / (Pi^2)
Short Meter 3.282806350 ((360 / (2 Pi))^2 / 10^n = 324 / (Pi^2) / 10
Long Meter 3.289868134 ((1 / 3) x (Pi^2)
Shorter” Palestinian Cubit 2.105515605 ft (1 / 4.6875) x (Pi^2)
Possible Ubaid Cubit of 2.368705056 ft (24 x (Pi^2) / 100
Additional Ubaid Cubit of 2.363620572 ft, based on original assessment of Ubaid Cubit as “.72 meters”

4. EGYPTIAN ROYAL FOOT FAMILY
Egyptian Royal Foot 1.152833216 ft
Hashimi Cubit / Pied du Roi 1.067438159 ft (1.152833216 x (100/108))
Petrie Stonehenge Unit 224.8373808 inches = 18.73644840 ft (20 / 1.067438159)
“Not-Phi” 1.618829140 ft (1728 / 1.067438159 / 10^n)

5. EGYPTIAN SACRED CUBIT FAMILY
Egyptian Sacred Cubit 2.091411007 ft (1.718873385 x 1.216733603)
Thom Mid Clyth Quantum 7.745966692 ft (2.091411007 x (27/100))

6. EGYPTIAN (SHORT) ROYAL CUBIT FAMILY
Royal Cubit 1.718873385 ft (diameteral unit to circumferential unit of 1.000000000 ft x (54/10))

7. “ALTERNATE E'” MEGALITHIC YARD FAMILY
Megalithic Yard 2.720174086 ft
Karnak Cubit 1.700109360 ft (2.720174976 / (16/10))
Ubaid Cubit (primary value uncertain) 2.361263000 ft (2.720174976 / (1152/1000))

8. PALESTINIAN CUBIT FAMILY
“Long” Palestianian Cubit 2.107038476 ft
“Shaved” Meter 3.280433688 ft ((57.29577951^2) / 1.000723277 / 1000) = ((6912 / 100) / 2.107038476)
Megalithic Cubit of Athanasios Angelopoulos?

9. “LE SERPENT ROUGE” FAMILY
“Le Serpent Rouge” (LSR) 1.676727943 ft

10. STONEHENGE OUTER SARCEN CIRCLE RADIUS/DIAMETER UNIT
True module uncertain but is known to appear in:
Stonehenge Outer Sarcen Circle Radius/Diameter (radius 51.95151515 ft)
Height Great Pyramid (unpaved) (height 481.0325483)
Jupiter Orbital Period, primary approximation (4329.2929298 days)

11. DRACONIC MEGALITHIC YARD FAMILY
Draconic Megalithic Yard 2.721223218 ft

12. INCIDENTAL MEGALITHIC YARD FAMILY
Incidental Megalithic Yard 2.719256444 ft

(13. IMPERIAL FOOT – Mainly Reserved as Reference Unit)
A few exceptions to the rule exist, one being the present model of the Mycerinus pyramid, projected height 216 ft Imperial, and potentially the Chephren Pyramid (base diagonal 1000 ft Imperial?)

Hopefully what this means is that all other ancient metrological units should fit into one of these families, and that there are really only 12 different ancient metrological units to know (along with “Imperial” as the reference unit).

Cheers!

–Luke Piwalker

Does the Munck Megalithic Yard Have a Use?

Lately I’ve been looking at some work by others regarding area and volume figures for the Great Pyramid – very interesting stuff.

However, I’m also reminded of some of things that happen in my own “realm” concerning this subject.

I don’t want to say that the ancients didn’t really care about surface area and volume of structures, that at least runs contrary to the idea that they are trying to post significant data wherever possible, but given the workings of metrology, there are some concerns that might be observed.

The Megalithic Yard is a strange animal, period. We have some six versions of it now counting the Squared Munck Megalithic Yard, which is probably the strangest of the lot.

The only Megalithic Yard that is really much worth squaring is Munck’s, which itself is not even valid unto its own system of numbers, yet not only can we square it, we can do a lot more with it exponentially, which is just not going to happen with any other proposed Megalithic Yard values that I’m aware of.

So we need the Squared Munck Megalithic Yard but we also need these other variations on the Megalithic Yard to keep things working, because of the other version’ lack of exponential function.

It’s been some years, but I think Munck introduced a few equations that work with the Munck Megalithic Yard of 2.719715671 ft, but they probably consisted of what I call “submarining”- the square of the square root of the Squared Munck Megalithic Yard times the square root of Pi or the Radian or some such thing, but I feel like that’s cheating, like it’s sneaking up under the rules to do something that we really don’t need to be doing in the first place.

However, there were hints that the Munck Megalithic Yard does have some functionality, and the clue is written into its very nature: Area figures in a single unit call for squaring a value. Legal “linear” Megalithic Yards like 2.720174976 may not be a pretty sight when we square them, but because of this relationship, if we swap in 2.719715671 as the Megalithic Yard just before calculating an area figure, then we often get a much more pleasing result.

This is true both at Stonehenge, and at the Great Pyramid, both of in which the Megalithic Yard is prevalent.

I’m generally hesitant to even bring this up for fear of just confusing people or even being accused of “making up the rules as I go along” but since in the last post I made several references to possible unusual forms of units that “may come with their own set of rules”, it helps bring to mind the Munck Megalithic Yard, which probably by far the most dramatic example of a unit “with its own set of rules”, and I know from experience that there is additional significant data we can on occasion recover from ancient sites by being observant of that.

If it helps any to offset any resulting confusion, as always the best “rule of thumb” might be that whatever works best in a given situation, is probably what was intended (keeping to our own “idioms” of course).

However all this does try to raise certain questions, and one of the first might be whether people who were that preoccupied with area and volume really have chosen the Megalithic Yard (of all things!) as the base unit of the Great Pyramid.

I would suggest that we at least look at the other aspects of a monument first, and not try to predicate linear measures like length and height on area or volume calculations.

–Luke Piwalker

A Metrological Round Up

I think a few metrological discoveries might have fallen through the cracks the past year. Early last November, I posted an incomplete compilation of which units belong to which metrological unit families, but at least several things are notably absent from it.

One has come to light again while working with projecting hexagonal figures onto Stonehenge, following what I believe to be rather important observations about geometry and metrology by drew at GHMB.

Essentially I think what drew is showing us is that Stonehenge is proportioned in places like a generic reference to hexagonal geometry, thus I’ve recently been experimenting to see what else hexagons might teach us about geometry and metrology if we project them onto the circles of Stonehenge.

“Not-Phi” = Egyptian Royal Foot

When we get to the Stonehenge outer bluestone circle, we see 1.618829140 (“Not-Phi”) showing up prominently, and showing how removed it is not from more conventional metrological figures such as the Harris-Stockdale Megalithic Foot

As before, the inner hexagon is made of six triangles with edges equal to the Radius, so Radius being 77.92727283 ft, the perimeter of the inner hexagon would be 77.92727283 x 6 = 467.5636369 ft.

This is an important number that was prominent in Munck’s work although it has been rarely seen of late, but it does have its reasons for being.

The triangles would have height of 77.92727283 / sqrt (4/3) = 67.48699792 and this intrigued me that we should see what looks like the Radian x Megalithic Foot (57.29577951 x 1.177245771 = 67.45121412 ft again so soon in this exercise.

The outer hexagon would thus have perimeter of 67.45121412 x 6 = 404.7072847, and that’s where things got very interesting, because 404.7072847 x 1618.829139.

…a long time ago I worked with tetrahedra, and adapted the surface area of sphere / surface area of circumscribed tetrahedron, 2.7201688946, to the Megalithic Yard value 2.720174976, such that for a generic sphere of surface area obtained for A=4Pi*r2 by making the Radian value the Radius value so that 4 Pi x 57.29577951^2 = 41252.96124 and 41252.96124 / 2.720699046 = surface area of tetrahedron 15162.63304; with the substitution of 2.720174976 for 2.720699046 we obtain 15165.55428 as a generic surface area for a circumscribed tetrahedron.

It’s been noted that 1.618829140 / 1.067438159 = 15165.555428 / 10^5, but perhaps it tends to get overlooked that 1.618829140 x 1.067438159 = 1728/1000.

So there is what it is – although it may keep trying to fall off the radar because it comes with different rules that a 1.622311470 ft Assyrian Cubit, 1.618829140 may be a real ancient metrological unit value, and what it really is would be the Hashimi Cubit / Egyptian Royal Foot.

As such, the value should be added to the list of metrological unit values under the Egyptian Royal Foot.

“Shaved” Meter = Palestinian Cubit

Also, awhile back it was observed somewhere in my writings that a meter of (57.29577951^2) / 1000 / 1.000723277 ft would be the second known member of the Palestinian Cubit family

3.280433687 x 2.107038476 = 6912 / 10^n is our proof of this.

Long Royal Cubit = Megalithic Foot

Apparently it has avoided mention, but because we know that the Long Royal Cubit (1.718873385 x 1.000723277) is synonymous with the Long Indus Foot, and the Long Indus Foot is in turn synonymous with the Megalithic Foot, then the Long Royal Cubit belongs to the Megalithic Foot family.

The Short Remen / Thoth Remen Family

Yes, dear reader, you heard that right. The Short Remen and Thoth Remen belong to the very same family of ancient metrological units, which seems to have been recently realized in essence back when the two related meter values were equated with one another.

Naturally, this family includes shorter unit versions based on the Remen such as the Short Greek Foot (10 / (Pi^2)) ft, but it also includes one of the shorter forms of the Palestinian Cubit, 2.105515605 ft, as opposed to the standard value of 2.107038476 ft.

Still Unaccounted For?

Two of the most important ancient units of measure that are still unaccounted in conventional historical terms for outside of several important variations on the Megalithic Yard would of course be 1.676727943, and the Stonehenge outer sarcen circle radius/diameter unit.

We know they exist because of all the pointers to them, but putting a name to them and determining the optimum unit values involved remains challenging, even when we are able to project the exact unit values.

Things were similar with the Egyptian Royal Foot. I used to think there was a separate unit that I jokingly called the “Ellifino”, which turned out to be 1.8 Hashimi Cubits, and then the Hashimi Cubit of 1.067438159 ft turned out to be 100/108 of the Egyptian Royal Foot, making them synonymous. Now we know that these units all belong to the same family along with Petrie’s Stonehenge Unit.

I have recently demonstrated that the height of the Great Pyramid would also be based on this later unit, whatever the correct quantity of units would be.

Our proof of this is that 10 times the outer sarcen circle diameter / height Great Pyramid (unpaved) = whole number or whole number x or / 10^n.

519.515151515 ft / 481.0325483 ft = 108/100.

I have proposed that the base unit may be an oversized Assyrian Cubit of 1.622311470 x 1.000723277 that comes with its own set of rules, as would an undersized Assyrian Cubit of 1.618829140 ft also apparently, but somehow this seems to remain purely speculative for lacking stronger proof.

(1.622311470 x 1.000723277 = 1.623484851 ft)

1.623484851 x 32 = 51.95151515

(1.623484851 x 1000) / 481.0325483 = 3375/10^n, but both of these conversion values seem a little bit strange. 32 as a conversion factor isn’t unheard of but 3375 is one of those numbers that it is so rare to see that it’s most likely best avoided.

As far as I was able to tell, we can probably file the Megalithic Cubit of Athanasios Angelopoulos under the standard Palestinian Cubit as well.

Unit Interactivity

There’s a great deal of interactivity between standard unit values, and while this may not help to identify units, it may help to identify their legitimacy and perhaps even sometimes their origins. I’ve written about this before as the “unit x times unit y” phenomenon and so forth as it became more noticeable when adding a few new units to the repertoire.

(So far I think the total number of true ancient units of measure may not be likely to exceed 12; I find it remarkable that we can reduce such a list of ancient units down to a figure this small).

I mention this here because it was was noted that Royal Cubits x Megalithic Yards = Stonehenge sarcen circle radius/diameter unit.

It was also noted that the inner sarcen circle circumference of Stonehenge (technically in units made from Megalithic Feet) / Thoth Remen = value in Egyptian Sacred Cubits.

We can reduce this to Megalithic Feet / Short Remen = Sacred Cubits.

Additionally, it’s recently been observed that Long Royal Cubit / Palestinian Cubit = 3 Draconic Megalithic Yards, which reduces to Megalithic Foot x Palestinian Cubit = Draconic Megalithic Yards.

Thus the pointers to the legitimacy of some of these units continue to accumulate.

We might wish to notice

As before, the inner hexagon is made of six triangles with edges equal to the Radius, so Radius being 77.92727283 ft, the perimeter of the inner hexagon would be 77.92727283 x 6 = 467.5636369 ft..

1.718873385 x 2.720174976 = 467.5636369 = 9 x 51.95151515.

Thus 46756.36369 has managed to receive honorable mention twice in the course of a single day. I am happy to see this because I’ve generally had a rather hard time finding 46756.36369 although we knew it was a rather important number because it was Munck’s “Grid Latitude” for the Mycerinus Pyramid.

Thus we now begin to find it has some metrological value – perhaps it could even prove to be a “Unifying Value” in the sense of Harris and Stockdale

A Rarely Mentioned Metrological Mystery

It might be time to start having another look at this because I don’t think it’s been discussed in awhile, but the base diagonal from Munck’s Great Pyramid model keeps trying to be some sort of metrological anomaly.

The value has been specified in my work as 1067.077718 ft, and yes it’s sort of a heartbreak that it couldn’t come out 1067.438159, but that’s the way it works out. We know some of why 1067.077718 is important mathematically, but metrologically it thus far seems rather enigmatic.

Since the discovery of the C value for the Venus Orbital Period at Stonehenge, I have wondered how many valid versions of the Petrie Stonehenge Unit there might actually be.

This doesn’t of course actually mean that the VOP C value or the Great Pyramid base diagonal at the pavement are metrological values, but what is intriguing here is that (24 x 10^n) / 1067.077718 = 224.9133272, Venus Orbital Period C, just as (24 x 10^n) / 1067.438159 = 224.8373808, Venus Orbital Period A.

Apparently then the Great Pyramid base diagonal can at least lay claim to being an astronomical value.

–Luke Piwalker