New Pyramid Theory: Khufu's Great Pyramid, its Building Grid, the Number 7 and the 'Diamond Matrix'
For thousands of years, scientists from around the world have tried to understand how the Egyptians designed and built the Great Pyramid of Giza – the last remaining of the seven wonders of the ancient world.
Now, an architect and researcher at the Norwegian University of Science and Technology (NTNU) says he has the answer to this ancient puzzle.
According to Ole Bryn, the Great Pyramid's building grid was developed based on the prime number seven – and the core of Khufu's 146.6 meters high monument is likely a step pyramid.
Khufu's Great Pyramid, located on the Giza Plateau, was constructed around 2600 BC. It was the tallest man-made structure in the world for over 3,800 years, making it what is likely the most studied build in the history of mankind. Over time, many theories have been put forward – some more plausible (although still not accepted by the mainstream) than others – as to how the Egyptians constructed the 'true' pyramids.
Ole J Bryn, an architect and associate professor in NTNU’s Faculty of Architecture and Fine Art, argues that modern day scholars have been so preoccupied by the weight of the estimated 2.3 million limestone blocks – which weight roughly 7 million tons – that they tend to overlook the other major problems the pyramid builders would have faced.
How did the Egyptians know exactly where to put the enormously heavy building blocks? And how was the master architect able to communicate detailed, highly precise plans to a workforce of 10,000 illiterate men?
In his paper, Bryn does not touch on how the ancient Egyptians would have put those enormously heavy building blocks in place – there are numerous theories about ramps and other suggestions already out there. Rather, the Norwegian scholar examined how the builders would have known where to put them.
“The need for precision is the same, whatever means one applies to get the masonry to the top,” he writes. And once it was decided where the blocks would have to go, then how was the master architect able to communicate these detailed, highly precise plans to a workforce of 10,000 illiterate men?
Bryn says that studying the plans from the thirty oldest Egyptian pyramids whilst keeping these two questions in mind, he discovered a precision system that made it possible for the Egyptians to reach the pyramid’s last and highest point – the apex point – with an impressive degree of accuracy.
“The Egyptians invented the modern building grid, by separating the structure’s measuring system from the physical building itself, thus introducing tolerance, as it is called in today’s engineering and architectural professions,” says Bryn.
In the 3rd millennium BC, the unit of measurement used to construct religious and royal structures was the Egyptian royal cubit (Rc). It represented the forearm of the Pharaoh, and was divided in 7 palms (p). The latter was then divided in four fingers, or digits. It wasn't until the late 19th century, when Flinders Petrie was the first to accurately survey the Giza Plateau and the Great Pyramid, that a precise number for the length of an Egyptian royal cubit (Rc) was established: 52.355 cm - Khufu's pyramid was 280 Rc hight.
Yet, 7 being a prime number, is problematic for a building grid. So how did the Egyptians solve this? “The Egyptians divided the pyramid in 7, which produced a 6-stepped core structure, with the seventh step replaced by the apex point,” writes Bryn. To produce a 3D building grid for this structure, one would need to divide 280 Rc by 7. As the Rc are divided into 7 palms, one can just change the units – from Rc to p. One palm is 4 fingers – the building grid becomes easily divisible.
Bryn points to the section of Khufu's pyramid as the strongest evidence for the division of the pyramid into 7 parts – or six mastabas (the part of the pyramid between to steps) and the apex point. “The Queen's chamber is placed precisely on top of the first mastaba, the King's chamber is on the second mastaba, and the Great Gallery forms a ramp between the first and second mastabas.”
These 6 mastabas would make up the core of the pyramid, and “the accreditation walls forming the stepped core of a true pyramid are made with horizontal laid masonry” - which would allow to transfer the building's grid vertically between the six steps, using nothing but a plumb line.
In 'Retracing Khufu’s Great Pyramid: The 'diamond matrix' and the number 7', published May 2010 in the Nordic Journal of Architectural Research, Bryn further discusses how the use of a 6-square grid master plan would have influenced the main building grid, and thereby the geometry of the Great Pyramid. It wasn't until the 1920s, when aerial photographs of the area were taken, that it was revealed that Khufu's pyramid is not set on a square base. Rather, as Bryn explains, “the centre line on each face is moved inwards by a short distance at the base.” (Surprised? Look for yourself, this is clearly visible in these satellite images of the Giza Plateau.)
Ole J. Bryn’s findings will be presented and explained at the exhibition The Apex Point in Trondheim, Norway from September 13 to October 1, and in a forthcoming book to be published in the spring of 2011.
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hello this is a real interesting article on forgeries
excellent article !
Museum looks really great.
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There are really lots of secrets in Egypt. I'm sure this is going to cost millions in auction.
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Comments
In fact Flinders Petrie already noted the modulus of 7 in the Great Pyramid in 1925, in his Nature journal article, and related it to the circular proportions of the architecture:
“The bases of some of the other pyramids are also known from my surveys. That of king Snefru and Meydum immediately... preceded the Great Pyramid, and was planned on a similar system of measures. Both have the proportions resulting from the height being the radius of a circle equal to the circuit of the base, the angles found being:
By Pi theory: 51*51’14”.3
Khufu’s pyramid 51* 50’ 40” +/- 1’5”
Sneferu’s pyramid 51* 52’ +/-2” ?
The dimensions found are:
Khufu’s, height 7, circuit 44, x 40 cubits.
Sneferu’s, height 7, circuit 44, x 25 cubits.
The modulus of design, being thus 40 or 25 cubits shows the deliberate intention to embody the proportions of 7 : 22.”
This new Norwegian article has possibly identified this modulus through other means, but his conclusion that circular proportions were not intentional but a by-product is not correct. The modulus 7 is identifiably there precisely because of the circular proportions.
Thats my take on this, as it was the take of I.E.S Edwards and Miroslav Verner and other top Egyptologists who also agreed that the circular proportions were the definining factor. My own 2008 work additionally suggests this was related to the architectural symbolic protection of Horus-Shenu - Horus-with-the shen, indicating "eternal royal encircling protection."
Best,
David Ian Lightbody
Archaeologist
See video link below for a new online lecture related to this (watch out for dodgy trailers before!).
www.veoh.com/browse/videos/category/travel_and_culture/watch/v20461797NHHNrqnz
My own publication on this subject (not for profit) is also on Heritage Key related to this:
heritage-key.com/publication/egyptian-tomb-architecture-archaeological-facts-pharaonic-circular-symbolism
It's available through Amazon.co.uk, or through the British Library website, or from British Archaeological Reports, Oxford.
Best!
Dave.
The author is correct in noting that a fundamental for accurate pyramid construction is a systematic measuring means in order for all four sides to reach the apex at a chosen height.
He is incorrect however in stating that this has not been understood by others studying this topic.
In my case published work over more than a decade.
However, accurate pyramid construction must use the corners as the primary reference.
An architect should understand this fundamental. It is supported by observing that of those pyramids which have some casing intact, none has 4 base sides of equal length, or a whole number of RC, or has 4 equal side slope angles, but all have corner edges running straight to the apex.
All Egyptian pyramids have simple height / centrepoint-corner proportions (the GP is 10:9) This allows the centrepoint-corner dimensions in all pyramids to be calculated at specific heights using a consistent formula (The Virtual Apex Method) and simple arithmetic. Corner edges are derived from these corner positions and from these the side slope is automatically formed.
Internal chambers are found at reference heights based on the pyramid’s proportion and the VAM, (not 7- see below) and are readily assembled during the period the façade is being added to the reference height. (In the GP the QC floor is at 37RC; the KC floor is at 82RC – both are VAM reference heights)
Egyptian measuring systems pre-date Pythagoras and knowledge of sqrt2. The division of Egyptian measures into 7 parts provides an alternative to sqrt2 as a square of side 10RC (70 palms), has a diagonal of 99 palms and therefore 99/70 = sqrt2.
Applying this fraction provided the AE with a simple means for calculating a virtual centrepoint-corner dimension from a side dimension when a base is covered and vital in pyramid design.
My Youtube video, ‘The Great Pyramid Building Challenge’ demonstrates the application of the Virtual Apex Method to construct a small solid pyramid with exactly the same proportions as the Great Pyramid using simple tools and without the apex as a reference. (My book details how all other aspects of the construction process economically follow this fundamental design.)
I have invited others to attempt the same using any alternative method, but no takers so far.
Any pyramid construction theory can be tested on this scale, as the same fundamental alignment problems are presented if the apex is not available as a reference, regardless of a pyramid’s size.
I maintain that the Virtual Apex Method is the only way of forming a solid pyramid of any size accurately, and must therefore include all those in Egypt.
Maybe Mr Bryn would like to have a go with his design or at least show my video at The Apex Point Exhibition.
Seamus Chapman
Why suggest the ancients lugged the enormous carved blocks, weighing more than two tons apiece, to build the upper portions of the great pyramids without mention of Drexel University scientist Michel Barsoum from Egypt?
He announced that some of the blocks were not carved at all, but were formed by pouring a concrete-like "geopolymer" that could be brought up in buckets.“There’s no way around it said Professor Hug when he told Science et Vie magazine. The study was published in the Journal of the American Ceramic Society. The pair believe that the concrete method was used only for the stones on the higher levels of the Pyramids. Extract:
'Soft limestone was quarried on the damp south side of the Giza Plateau. This was then dissolved in large, Nile-fed pools until it became a watery slurry. Lime from fireplace ash and salt were mixed in with it. The water evaporated, leaving a moist, clay-like mixture. This wet “concrete” would have been carried to the site and packed into wooden moulds where it would set hard in a few days. Mr Davidovits and his team at the Geopolymer Institute at Saint-Quentin tested the method recently, producing a large block of concrete limestone in ten days.
Intriguing proposition. Curiously, while I have nothing to comment about the proposed ideas, the cross section prompted what may be a new idea about how to actually erect the thing, and I can't think of a better place to float it.
Start the actual construction at a corner, and raise the structure, with facing stones, at the same time you build the interior layers out from the same corner. Think of building a pyramid with one meter blocks; the surface at the corner would never be more than one meter higher than the surface you are standing on, no matter how high you build (assuming, of course, that you have the good sense to pace the interior construction stepwise to keep up with the first corner) and you automatically end up with an ideal work platform from which to place the pyramidion! Then all you have to do is continue "wrapping" the surfacing , still only one level above your feet, as you finish your way back down the opposite (or concievably, an adjacent) corner.
This suggests the possibility that the ramp (assuming one was used) would be built temporarily out of the very stones that went into the pyramid itself, which would be cannibalized as the project was completed.
I wish you all would stop calling the great pyramid,"Khufu's pyramid".The crayon hieroglyphs that started this fantasy were placed there by a scoundrel named Vyse who was just trying to make a name for himself.If you dated the residue that would be quite clear.I just cannot believe that anyone with half a brain would buy Vyse's lies when presented with the facts surrounding the story,I mean he actually misspelled the hieroglyphs.If you need a builder and a date for construction so bad that you can't sleep at night let's say it was built oh ...3000 years ago by Santa Claus.Idiots.
MD, I like the graphics. Do you have a link to this diagram? Can't see all of it.
Regards
Nick
http://www.mdsign.nl/davinci-vitrivius-freemasons.jpg
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