The Construction of the Pyramids

Despite the photographic evidence below, I’m still on the side of human construction for the pyramids. I’ve blogged previously about Wallace Wallington, the contractor who moves 20 ton blocks by himself, in earlier posts. This time around I thought I’d expose readers to a scholarly article I came across as I prep for my ancient Egypt course that I’ll be teaching this Spring. It’s an insightful piece from the Journal of the Society of Architectural Historians called “Building Cheops’ Pyramid.” Enjoy, earthlings.

Careful with that, ET!

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71 thoughts on “The Construction of the Pyramids

  1. One of my people at work is a devoted Sitchenite. There’s no talking to her. It’s literally her religion now. But my question is, have you read any books or articles by Joseph Davidovitz? He is a French scientist who has been postulating for almost 40 years that the Egyptians could dis-aggragate stone and re-form it into the desired shape. In other words, the blocks were poured into molds by workers hauling slurry. No need for big ramps. It also explains the closeness of the blocks. Interesting. Thanks.

    • Yes; I show a short video of his theory in the Ancient Egypt class I teach at a local university. He doesn’t argue that all the blocks were concrete, though. I think his view works as ONE of several ancient technologies that could (theoretically) have gone into pyramid construction. I think the best overall explanation is that of Houdin (internal ramp).

  2. http://www.timstouse.com/EarthHistory/Egypt/GreatPyramid/interestingfacts.htm

    Notice the 13th point under general Center of Land Mass..Would anyone care to explain how the Egyptians figured this out? I am not an advocate of Stichen’s work.However I do think there might be something to the ancient astronaut theories.Am I wrong in stating that ancient cultures from around the world speak of beings from the heavens coming down and helping human advancement?

    • personally I’d say it means nothing. There are dozens of pyramids all over lower Egypt and clustered around the lower delta area. We only think this location is special because it’s the tallest. So what?

      • But the giza pyramids are still standing / any other pyramids built by humans in egypt are crumbling that should show you humans aren’t very bright

        • wrong – one several counts. There are a number of pyramids in good shape in Egypt, not just Giza. And think about your logic (“something really big long ago is still standing, so it must have been made by aliens”). I would suggest doing some reading on pyramid evolution. The various pyramids in Egypt (including Giza) show a very discernible development, at times trial-and-error. We know how the technology began and progressed from the pyramids themselves.

    • I could add one more thought. All this “center of land mass” notion proves is that the pyramid is *located* there. It doesn’t prove that the Egyptians *knew* the location was the center of anything. Correlation does not = causation.

  3. I might be wrong but I think the center of land mass means if you take a line going east to west and north to south around the entire earth the great pyramid is at the center of the greatest land mass on earth..So are you saying the Egyptians just got lucky putting it there?There is only one spot on earth they could have built the pyramid to achieve this center of land mass and they just happened build it there.It seems to me there is no way this center of land mass could be known without some sort of satellite mapping technology..Something would have to be able to view the whole earth from above do the calculations in order to achieve this..And i am not implying the Egyptians knew this I am asking how they could have possibly known this.

    • the only reason anyone would *think* it’s noteworthy is that it’s THIS pyramid. No one would care if it were Menkaure’s. Yes, I think there is zero evidence that it was planned. I’d think it more interesting if it were dead center. But at best what would that prove? That the Egyptians could mathematically calculate the circumference of the earth before the ancient Greeks did it (Eratosthenes, 3rd century BC). It wouldn’t be any more “alien” or supernatural than when Eratosthenes did it.

  4. I disagree because a person could know the circumference of the earth and that in no way would help that person locate the clm..How does knowing the circumference tell a person where all of the continents are located on the earth and what size the continents are?

    • this tells me you don’t understand the math that would be used. If you knew the circumference of the earth, you’d also know the parameters of PARTS of the earth, and you’d be able to divide your slice of the earth into mathematical units. All you need is an arbitrary starting point. Oh, well.

  5. Hi Mike, i don’t want to get sucked in to a big online debate, but i wanted to (collegially) offer my subjective observations of your broader work. You come across as someone who is trying to defend religion, and the defense you offer appears to focus on micro issues at the expense of the bigger picture. What do you think is going to happen when all religion is finally disproved (there are pyramids in Egypt far older than the 5000-6000 years our current civilization is presumed to have existed for). These sites are now primarily military installations now. Do you not think its coincidence that most Egyptian Scholars are also Muslims? Vested interested in sustaining the current paradigm don’t you think?

    The Mayans, the Hopi Indians, the Egyptians and the Sumerians all echo some very similar sentiments and there are too many correlations between these independent cultures, which are in turn are mentioned at least in parts of the old testament for it to all be coincidence. I don’t doubt you are correct in many things you say but you simply cannot offer an explanation for EVERYTHING that so far remains ‘unexplained’ and which implies interaction with beings of high intelligence.

    For instance i’d love to hear your explanation as to how the Dogon tribe in Africa understood the star Sirius to comprise two individual stars, how they understood the duration of years fo Sirius B to revolve around Sirius A, and how they knew it was ‘very old and heavy/dense’ (its a white dwarf). This tribe also possessed other ‘interesting’ celestial information such as the order of planets from Pluto to Earth, number of planets, etc. Why would they know the order of the planets, let alone the planets themselves, as you approach earth from outer space?? They knew this 700 years, whilst much of our science has only confirmed this in the last 50-100 years. And this is but one baffling example of many…

    I look forward to reading more of your work on this blog. Keep up the interesting research!

    • A few notes:

      1. Writers across religious boundaries contribute either coherent material or not. Their faith has nothing to do with whether than can think clearly, since such matters often must defer to presuppositions.
      2. I fail to see how chronology (Egypt being older in terms of civilization) would affect what you think it would In other words, your “challenge” here lacks coherence. Show me why the cause and effect you presume is coherent. For example, who cares if most Egyptologists are Muslims? (It’s actually probably not true, since it was Europe that first made Egyptology an academic discipline). Why would it matter? Does it matter if most heart surgeons aren’t Muslims? Where is the coherence?
      3. You write: “The Mayans, the Hopi Indians, the Egyptians and the Sumerians all echo some very similar sentiments” — exactly what sentiments are you referring to? Do you assume they were irreligious? (hardly) or that they would have cared if the Egyptian civilization was older? I don’t see the coherence.
      4. On your loving to see what I’d say about the Dogon: http://michaelsheiser.com/PaleoBabble/2009/06/seriously-the-dogon-and-sirius/

  6. coherence on my part, or equally possibly because you’re trying to trivialize certain aspects of my statement to discredit me.

    I should clarify that i was referring EGYPTIAN Egyptologists, not Egyptologists as a whole. Regardless, if you can’t see how an field with a figurehead (in this case Zawi Hawass) with a fundamental association to certain religious paradigm, (in this case the Muslim faith) which stands to be radically shifted by the very work undertaken by participants in the field he essentially administers, ISN’T a conflict of interest, there is literally no point in me going any further as you’re clearly not open to discussing the subject rationally. As im sure you’re aware Zawi Hawass essentially controls who researches what in Egypt and why. Now if say, something (man made) were to exist that would threaten that ideology, ie the existence of pyramids older than civilisation as we know it, wouldn’t that then provoke some interesting questions about the current socio-religious paradigm? One that as a Muslim he devoutly follows? Bear in mind also that ultimately, permission is dictated by the Egyptian government. If the work is potentially going to challenge the Muslim faith, do you really think it’s going to be permitted? This is a broader group of people with (an admittedly) fundamental component that in this day and age, chops off the heads of infidels! Don’t take that to mean i consider all Muslims fundamentalists, but that factor is relevant in painting the broader picture here. Just to clarify, the ruins im talking about are those of the first dynasty, which predate Saqqara. Can you explain to me why these are the only pyramids in Egypt to be enclosed by Military fortifications? I’d sure like to know…

    Similarly, if you can’t make the connection that (in the context of my first statement) this issue of chronology is intrinsically linked to this conflict of interest, i should just quit now.

    This whole issue and your blind faith reaction/explanations/rationalisations remind me of how the Catholic Church reacted when Galileo contended that the world was round and not flat, and that the solar system was heliocentric and not geocentric. We don’t know everything, and the paradigm must at some point change. I don’t pretend to know how its going to change, but to blindly defend it in the face of so many (way beyond the issue of pyramid construction) questions which cannot be accounted for in the current body of scientific and historical knowledge, is tantamount to suppression of the truth. You of all people have to concede that there are some things that humans still do not (i personalyl believe in the scheme of things we’re still in the process of climbing down from the trees – the world is still based on the notion of money and burning dead dinosaurs even though we know it will eventually destroy us and the earth!) and where historically these things have been attributed to “the gods”, i reject that 100%. While i don’t believe the popular notion of god being an old man in the clouds with a beard and a white toga, i certainly believe that there are forms of higher intelligence out there. If you understand the finite nature of stars, galaxies, and the constantly expanding universe, it’s irrational and illogical to presume that none of “this” has happened before.

    Whether or not this higher intelligence constructed the pyramids is neither here nor there. This is the broader picture i alluded to you ignoring in my first post, and this debate is manifest evidence of the trivialisation and micro-compartmentalisation of the bigger issue i also alluded to in my first post.

    • since Egypt is a Muslim country, I’d expect most Egyptian Egyptologists to be Muslim. That really means nothing, since they have no control over the discipline — Egyptology has been a flourishing discipline since the days of Napoleon. There are also many Europeans and Americans working with Egyptians at the highest levels.

    • I should also add that I know of few Christians in Egyptology, though I do know a few. This notion you have of a religious filter in Egyptology is incoherent.

  7. I forgot to mention that western science was only able to confirm the existence of Sirius B in 1862. Admittedly i didn’t see your post about the Dogons and you’re alternative hypothesis as to how they came across this information, but you still fail to explain how they knew that Sirius B was composed of the heaviest matter in the universe (not completely accurate admittedly, but not far off!) or how they knew the reverse order of the planets in relation to earth. We only discovered Pluto (i think it was Pluto, correct me if im wrong) in the latter half of this century, so how did they know this then?

    I’m continuing to read your blog and learning some new things and gaining a different perspective along the way, so keep up the good work!

  8. Mike, I’m at pains to point out that im honestly not trying to provoke a reaction from you or anyone else who may read this and that nothing i have posted has been with intended sarcasm or ill intent. Everyone’s entitled to their own view after all. I think ater this though i will think long and hard before adding anything to your blog. This is going to be a case of “agree to disagree”.

    But….

    I find your last point a little hard to swallow, particularly when you have posted commentary which seems to validate what im saying. See here:

    http://michaelsheiser.com/PaleoBabble/2009/08/close-mindedness-thy-name-is-zahi-hawass/

    The last sentence of that link is particularly relevant;

    “…Dr Zahi Hawass, Secretary General of Egypt’s Supreme Council of Antiquities has been quick to dismiss the discovery: “There are no new discoveries to be made at Giza”, he stated. “We know everything about the plateau – amateurs cannot find anything new….”

    That statement infers that ZH (and by association the ministry/movement he administers) is at best, dismissive of new discoveries by external parties in this area. Assuming the “we” he refers to is the Supreme Council of Antiquities, that alone validates what I’m saying. The second statement in which he proclaims to know everything there is to know about Giza simply supports the point i was trying to make about protecting the Muslim teachings. There may be nothing at Giza which would change the Muslim teachings, but whose to say that the attitude adopted on this issue isn’t uniformly applied to any contentious area of research? What i don’t understand is how a credible scientist and academic can presume to know everything. Closed behaviour of this sort suggests he is protecting something; whether it’s simple national pride or the principle tenets of the Muslim faith aren’t clear on the facts of this case alone, however I consider that to a certain extent, the two possible motives are related.

    Regards

    • Please — like I’m saying there are no more things to discover. Give me a break.

      What I’m, saying is that a number of engineers have taken a close look at the pyramids. They are not an engineering problem so much as they have been a logistical problem. The latter is fading fast ih wake of Houdin’s theory.

      Regarding provoking a reaction. I didn’t feel that way, but I do a bit to this last reply. I try to be as brief and plain as I can in replies. I don’t have the time to write much, so I try and cut to the chase.

  9. there are hundreds of pyramids that have been discovered all over the world. the reason that these specific three are of note is because after meticulous examination, by all logic we know, they shouldn’t be there – but they are. mainstream archaeology and egyptology claim that the great pyramid, for one, was built 4500 years ago by a civilization that for all intents and purposes did not have the wheel, were realtively recently out of the stone age, had no knowledge of the concept of pi, didn’t know the world was spherical, certainly had no machines, and had almost nothing at their disposal to accomplish this aside from stone tools and ropes. according to mainstream egyptology’s time schedule, 2.3 million limestone blocks (each weighing in excess of a few tons and some much much more) were quarried and carried across the nile river – each already being exactly the right size for where it ended up in the pyramid – in 20 years and put exactly in place. if one does the math, a stone would have had to have been placed every 4.5 seconds non-stop, day and night for 20 years, the highest being 480 feet up. each of the sides of the great pyramid (0.01% difference in length) is aligned perfectly with the four cardinal directions. the forementioned height of the pyramid is the same as the mean altitude above sea level of the entire earth. the pyramid itself utilizes a slope of exactly 53 degrees (4/pi) to achieve a mathematical representation of the entire northern hemisphere on a scale of 1:43200. more specifically, the relationship of its circumference to its height is the same as that of the earth’s circumference to its radius from the north pole. furthermore, if one divides the perimeter of the pyramid by its height, one gets 2pi. each of the sides of the great pyramid is cuved inward at its base. this slight curvature matches precisely that of the earth. all three of the pyramids at giza are a ground map of orion’s belt, each corresponding perfectly to angle, position and size of each of the three stars (alnitak, alnilam and mintaka). the position of these three stars in the sky locked perfectly over head in the southern sky in 10,500bc (with the nile river lining up to illustrate the milky way). this may sound like a coincidence, but this happens to be the same age from which the sphinx (originally a lion) is dated due to water erosion (occurring no later than 10,500bc) and position. by position, i mean that as the sphinx gazes east, and as it is in the form of a lion, it would have been absurd to construct a monument in the form of a lion in the age of taurus, when egyptologists say it was built. the age of leo was last seen in, yep, 10,500bc. it was an equinoxial marker gazing at its own constellation as the sun rose in front of it. to deny these very few examples and categorize them as coincidence would be irrational. there have been engineers, machinists, archaeologists and physicists who have stepped forward and said that we could not recreate these types of structures even today. others have studied the giza plateau and have found machine cuts on structures. notice i have said nothing about nibiru, nothing about the annunaki and nothing about astronauts. what i’m trying to demonstrate here is that it looks like there was a culture on earth who erected these and many other structures around the world who were far more advanced than we could imagine, and who lived longer ago than conventional egyptologists ever contended. the question is, where did they go? robert bauval, graham hancock, john anthony west, giorgio tsoukalos and, of course, erich von daniken do a great job entertaining this question.

  10. “if one does the math, a stone would have had to have been placed every 4.5 seconds non-stop, day and night for 20 years, the highest being 480 feet up.”

    Oh, may I try (full disclosure: I am not a scientist/engineer/mathematician)?

    Let’s see,
    2,300,000 blocks at 20 years.

    Okay:
    2.3 million blocks / 20 yr = 115,000 blocks/yr

    115,000 (blocks/yr) / 365 days = 315 blocks/day

    315 (blocks/day) / 24 hours = 13 blocks/hour

    13 (blocks/hour) / 60 min = 0.22 blocks/min

    0.22 (blocks/min) / 60 sec = 0.004 blocks/sec

    So that means they would have to set a block every 4/1000 th of a second…no, that is not meaningful…how about 1/0.004, which yields:

    (roughly) 270 seconds per block? Or better, 4.5 minutes per block.

    These guys (http://news.discovery.com/archaeology/pyramids-tombs-giza-egypt.html) say it took 30 years, which yields:

    6.85 minutes per block.

    Also, these guys (http://www.nationalgeographic.com/pyramids/khufu.html) estimate “workers would have had to set a block every two and a half minutes.” Guess they took more time-off.

    In any event, the assertion is false that the math dictates a block needs to be set every “4.5 seconds” (barring a math error or some such, in which case you have my apologies for the confusion).

  11. Just got a link to you from a fellow PoF forum aquaintence.
    Interesting stuff …
    I’ve read a lot of it previously but don’t mind refreshers.
    The Spynx thing need more than erosion evidence … it needs pollin dating evidence. Wind and sand erosion versus water erosion are not so easily distinguished in a desert and the source of the categorizing it as water erosion is not completely reputable.

    I agree daniken and friends are entertaining but factuality is dubious at best.

    I do find it strange … that the Egyptologists don’t push to test the geopolymer theory with actual stone from the quaries of Giza.
    http://www.geopolymer.org/category/archaeology/pyramids seems pretty concrete [no pun unless you like puns] as far as the simplicity of the science goes.

    A lost technology of the ancients makes more sense than aliens. I do think there could have been an ancient globalization of sorts at one time allowing this technology to be used in the Americas too. The simple reason pyramids are all over the world is that a pyramid is a basic geometric shape and as math improved … so did construction. … again … no magic aliens needed.
    Just respect for the intellect of ancient man. He had at least 70,000 years to think up how to do it.

  12. i’m more partial to the ancient technology theory than aliens as well. and pons, it wasn’t a math error; it was a typing one. i typed the word “seconds” when i meant to type the word “minutes.” this begs one to read it again with the correction. is it still not outrageous that a stone was placed more frequently than every five minutes for twenty years straight, nonstop from people who barely have any tools (pretty much what i attempted to say in the first place, haha)? does that not completely befuddle anyone else? is everything but my clerical error being chalked up to coincidence? it is also interesting that while it is agreed upon that the egyptians of 4000 years ago didn’t have means of global communication or transportation, another pyramid (this one almost as befuddling) stands exactly the same size over 7000 miles away (teotihuacan). and no, wind and sand erosion are not easily distinguishable from one another, but they are distinguishable as separate from water erosion.

    i see how someone else suggests that the stones were cast. that’s right, cast! this suggests that the ancients had the equipment necessary to bring limestone to a liquid and pour it into place (a theory entertained at puma punku in bolivia) employing an advanced technology that was later lost while conventional archaeology says these people were relatively recently out of the stone age. this type of method is today considered for advanced high-tech composites and ceramic applications! this would be an amazing discovery, and i would be the first to embrace it. thanks for the geopolymer article (ps – i love puns)! if this technology existed, it again begs the question: where did the people who possessed this technology go? were they actually the same people who lived near the nile in the second millenium bc?

  13. Thank you MSH, your website rocks! Your brief tutorials on the Sumerian language coupled with the scholarly resources that you linked are fantastic. Your responses to Mr. Zecharia Sitchin’s work (especially your translation citations for the VA-243 piece) are nothing short of superb.

    Thank you for your work in establishing this website, it makes it easy to find logical and objective sources when it comes to evaluating assertions often made by Ancient Astronaut Theorists. (Of course, I also enjoy Ancient Sumerian history, and having an expert so willing to provide such a website…well, thank you.)

    —-

    Jeff, I’m curious about your statement @ 3 May 2010 at 12:16 AM.:

    “the pyramid itself utilizes a slope of exactly 53 degrees (4/pi)…”

    What does the 4/PI signify?
    a) a simple number to be multiplied by 53 degrees?
    b) the slope in radians, equivalent to 53 degrees?
    c) the tangent of the slope of 53 degrees?
    d) something else?

    If (a), then the statement is meaningless because it just represents a coefficient attached to an arbitrary angle.

    If (b), then it is false, as 53 (deg) = 53 PI/180 (rad) = 0.2944 PI (rad) != 4/PI (rad)

    from: http://www.teacherschoice.com.au/maths_library/angles/angles.htm
    calculator: http://www.marlenesite.com/math/trigonometry/adegrees2radians.asp

    If (c), then it is also false:

    Using PI = 3.141592654
    from: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html

    Then

    tangent of “exactly 53 degrees” = tan (53 deg) = tan (53 PI/180 rad) = 1.32704

    and

    4/PI = 1.27324

    Since 1.32704 != 1.27324, then the slope of “exactly 53 degrees” does not equal 4/PI.

    If (d), then please specify (and source by link please) as I am most curious about this assumed relationship claim. Appreciate it, thanks.

  14. Orthodox archaeology claims without a flinch that the great pyramid builders had no sophisticated understanding of the concept of Pi (Beckmann, 43-46), and they furthermore claim that it wasn’t accurately quantified until the work of much later Egyptians, or not even until the Greeks over 2000 years later, yet there are plenty of instances of a very sophisticated use of Pi in the pyramid’s construction dealing with things like its perimeter, its height and the dimensions of the king’s chamber, among others (Hancock, 273-350). I simply could have picked another occurrence of Pi to illustrate its usage as being one of many things that orthodox archaeology chalks up to coincidence, and perhaps one less readily dismissed. That being said, I will also be the first to agree that Pi usage is NOT a smoking gun from a lost earlier civilization, but it was never the most compelling of what conventional archaeology would call an “oop” (out of place), and i never meant for it to be the crux of my argument, because there are plenty of far more compelling “oop”s at Giza and all over the world that conventional archaeology is, for all intents and purposes, ignoring.

    Beckmann, Petr. “A History of Pi.” New York, NY: 1971.

    Hancock, Graham. “Fingerprints of the Gods.” New York, NY: 1995.

  15. Jeff @ 7 May 2010 at 11:49 PM
    “i typed the word “seconds” when i meant to type the word “minutes.” “

    No worries Jeff, I make typos all the time. So 4.5 seconds should read 4.5 minutes per block — got it, thanks Jeff.

    “is it still not outrageous that a stone was placed more frequently than every five minutes for twenty years straight, nonstop from people who barely have any tools (pretty much what i attempted to say in the first place, haha)?”

    That is an impressive rate, but it is an average measure, not a literal procedure. In other words, a single team did not likely place an individual block every 4.5 minutes. More likely, several teams placed several blocks every day (or work shift) — 4.5 min per block is what the workers would need to have averaged.

    Consider something like this:

    4.5 min/blk translates to about:
    320 blk/day (for twenty years, non-stop, etc)
    380 blk/day (for twenty years, where each year consists of 300 days-of-work and 65 days-off)
    400 blk/day (for twenty years, same as above but also accounting for mistakes and setbacks).

    Given all that:

    400 blk/day divided among (say) 20 teams –>

    20 blk/day per team, where each work-day for a team is (say) a 10 hour shift –>

    20 blk/10 hr per team –> 2 blk/hr per team –> 1 blk every half-hour per team.

    Further, each team could have two crews, where each crew works only 5 hours a day.

    Bottom line, here is a scenario where a team of workers gets 30 minutes to place each block, from the time they receive it (where each worker gets 65 days-off a year, and executes actual labor of 5 hours a day).

    Adjust some parameters:
    *increase the teams to 40, the rate is 1 blk/hr
    *then increase the construction time from 20 years to 25, 0.75 blk/hr (or 1 hr and 13 min per block)
    *then increase the shift to 12 hours (6 hours per crew), 0.64 blk/hr (or 1 hr and 33 minutes per block).

    (something like that anyway)

  16. we can play with the factors (time, number of individuals, weight of the stones, distance hauled, etc) all we want and continuously assume more and more people were involved, and in your calculations you seem to be asserting that i disagree the pyramids were built at all, which i obviously don’t, but it has become apparent that those who did build the pyramids at giza were by no means “one step out of the stone age,” as it has been referred to in the past, but instead master builders, surveyors, architects, astronomers and engineers. it’s not so much a question of timing and head-count, but instead a question of primitivism and foresight. the fact that it’s feasible for a large group of people to build a pyramid doesn’t compromise this. these three were done with such exacting results, and the rest of the pyramids found all over egypt, which probably utilized some form of your methods of construction, absolutely pale in comparison to the three at giza. somehow, this includes pyramids attributed to dynasties that came to pass AFTER the fourth dynasty and its three at giza. this begs the obvious question, if each dynasty stood on the shoulders of the last and advanced its ability to build its “tombs,” why have the later dynasties’ pyramids not withstood time as the fourth dynasty’s have? since they were such a feat, why are there no markings indicating to whom they belonged? if i was a pharaoh in charge of building those, i would make sure everyone knew it was i who built them. the reason may be that these were INHERETED by the fourth dynasty kings instead of built by them. people as primitive as orthodox egyptology claims could not have done this – even at 1 bock per hour and a half, which is being generous given the time schedule. yet people still think that those with only copper tools and some rope at their disposal lifted tonnage of limestone to almost 500ft, not to mention how each stone was exactly the size it needed to be, and also not to mention the distance from which said stones were quarried, and they did it so perfectly that they remained unchanged for thousands of years. have you seen the chambers and shafts inside the great pyramid? the way they were constructed couldn’t be duplicated even today. they were basically rolex watches built to the size of mountains.

  17. Jeff @ 10 May 2010 at 9:43 PM.
    “That being said, I will also be the first to agree that Pi usage is NOT a smoking gun from a lost earlier civilization, but it was never the most compelling of what conventional archaeology would call an “oop” (out of place), and i never meant for it to be the crux of my argument, because there are plenty of far more compelling “oop”s at Giza and all over the world that conventional archaeology is, for all intents and purposes, ignoring.”

    Agree with you, Jeff, about PI usage in the Great Pyramid not being a “smoking gun” for an “out of place” moment. Here is a simple method of construction-design for the Great Pyramid, that incorporates relationships of PI (and other notable ratios as well) without the builder having to know about the existence of such relationships.

    From:
    http://www.math.dartmouth.edu/~matc/math5.geometry/unit2/unit2.html#Egyptian%20Triangle (scroll down to the section entitled: “Pizza-Cutter Theory”).

    “The Pizza-Cutter Theory

    Suppose that the Egyptians didn’t know anything about but laid out the pyramid using a measuring wheel, such as those used today to measure distances along the ground.

    Take a wheel of any diameter and lay out a square base one revolution on a side. Then make the pyramid height equal to two diameters

    By this simple means you get a pyramid having the exact shape of the Great Pyramid containing perimeter-squaring of the circle and area squaring of the circle and, for no extra cost, the golden ratio!”

    Applying this to the Great Pyramid, if the circumference of the measuring wheel were (say) 1 cubit, then:

    440 revolutions (or 440 X 2 PI radians) = 440 cubits (total length)
    220 revolutions (or 220 X 1 PI radians) = 220 cubits (1/2 total or leg-length)

    Thus, the leg-length would be a multiple of PI.

    For the height, take 2 diameters of the measuring wheel and multiply by a scaling factor of 440, or:

    Height = scaling factor X 2 X d = 440 X 2 X (1 cubit / PI) = 280.11 cubits

    (note: we know that d = circumference / PI, the Egyptians could have simply measured the wheel to get diameter).

    <a href="http://www.mathopenref.com/coordslope.html"To find slope we simply divide rise over run, or:

    Height/leg-length = 280.11/220 = scaling factor X 4/PI = 1.2732

    This renders an angle of:

    arctan(1.2732) = 51.85 deg = 51 deg 51 min 14.3 sec

    In short, building in this manner would guarantee the incorporation of the PI relationship (and other famous ratios), even if the builders had no direct knowledge of PI.

    Just a quick note about choosing two diameters for height:

    1 d yields a height and slope of: 140.06 cubits and 32.48 deg (not impressive)
    2 d yields a height and slope of: 280.11 cubits and 51.85 deg
    3 d yields a height and slope of: 420.17 cubits and 62.36 deg (too expensive)

    So, using two diameters of the measuring wheel (multiplied by the scaling-factor) to get the height would guarantee an angle above 45 deg and by not gong larger than two diameters, the expense and time-of-completion are reasonable.

    IMHO:

    The Great Pyramid is without a doubt the Masterpiece of the Egyptian pyramid-making engineering. Given centuries of pyramid-making and stone-cutting traditions prior to the construction of the Great Pyramid, perhaps a confluence circumstances — ability, knowledge, wealth, stability, continuance — gave rise to such a masterpiece.

  18. Jeff @ 3 May 2010 at 12:16 AM.
    the aforementioned height of the pyramid [480 ft] is the same as the mean altitude above sea level of the entire earth.

    This is an interesting assertion, and it is repeated on a variety of non-scientific sites. However, none of those sites source any scientific data as to what the “mean altitude above sea level” was at the time of construction.

    Are you able to source the scientific data that “the mean altitude above sea level of the entire earth” was 480 ft at the time of the construction of the Great Pyramid (please feel free to pick whatever construction date you wish)?

  19. Jeff @ 3 May 2010 at 12:16 AM.
    …to achieve a mathematical representation of the entire northern hemisphere on a scale of 1:43200.

    Given:

    * mean polar radius of the Earth is 6,356.7523 km or 6,356,752.3 m
    * orignial height of the Great Pyramid of Giza was 146.478 m
    * scale of 1/43,200

    Then 6,356,752.3 m / 43,200 = 147 m

    Since 147 m is close to the suspected original height of the pyramid, why stop at the northern hemisphere? This height roughly corresponds to the scale of the entire Earth Polar Radius.

    However, any measurement multiplied by an arbitrary scaling factor will yield any result. For example, all of these measurements correspond to the height of the Pyramid (all in meters):

    A scaling factor of 2,615,000 (rounded), corresponds to: distance of the Earth / Moon.
    A scaling factor of 486,300 (rounded), corresponds to: Diameter of Jupiter.
    A scaling factor of 43,400 (rounded), corresponds to: Equatorial Radius of the Earth.
    A scaling factor of 43,200 (rounded), corresponds to: Polar Radius of the Earth.
    A scaling factor of 41,200 (rounded), corresponds to: Radius of Venus.
    A scaling factor of 18,400 (rounded), corresponds to: Diameter of Triton.
    A scaling factor of 6,500 (rounded), corresponds to: Diameter of Ceres.
    A scaling factor of 75 (rounded), corresponds to: Depth of Marianas Trench.
    A scaling factor of 29 (rounded), corresponds to: Ave Depth of the Pacific Ocean.
    A scaling factor of 14 (rounded), corresponds to: Ave Thickness of the Antarctic Ice.
    A scaling factor of x (rounded), corresponds to: y.
    …etc.

    According to this source, the scaling factor of 43,200 is not arbitrary, but linked to the precession of the Earth. The idea being that a 60 deg arc along the ecliptic plain takes 4,320 years. Multiply this by 100 and one comes to 43,200 years. Finally, ignore the units and disregard that this parameter is not a scaling factor but a time factor.

    Such a construction still has arbitrary properties and is quite contrived. Picking an arbitrary 60 deg segment (why not 120 deg or 180 deg, which exactly equals PI radians?) and multiplying the time it takes to travel that segment by an arbitrary factor of 100 (why not 1,000 or 10 or 1/10?), then ignoring the time parameter and arbitrarily stripping the quantity of its units (which are years) is hardly the work of master engineers.

    Bottom line: The scaling factor is arbitrary, either by means of random choice or by means of contrived selections.

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