The geometric design of the Giza pyramids

[robincook]

I have published a website -

url deleted

This site examines the geometrical design of the Giza pyramids, summarizing the findings of a number of authors,  as well as describing  the latest astronomical findings. I have approached egyptologists but with little response so far - perhaps they write me off as a fringe author. However I continue to plough ahead hoping to receive feedback on what I have written. It occurred to me that if I were to post on a scientific forum I might get a more impartial response.  I hope it's ok to post in the general philosophy section - I don't know which would be a better section to post in.

 

robin

[swansont]

53 minutes ago, robincook said:

I have published a website

!

Moderator Note

And our rules prohibit making threads to advertise sites. You need to post the information here

 

[robincook]

Dear Swansont,

Ok I'll try to summarize (assuming readers have at least a passing acquaintance with the Giza complex - if not refer to Wikipedia to get up to speed).

Most people today see pyramids as the useless products of a vainglorious elite (albeit at the same time being the focus of popular mysticism). However, if we concentrate on the architectural design of pyramids some surprising relations emerge which are yet to be explained.

Egypt is viewed as a 'craft culture' - assiduously building giant structures in cut stone using the simplest of tools and methods. The Egyptians pushed the limits of what man can achieve using such means. But they were also very meticulous in realizing their designs, and in pyramid complexes we are presented with a large amount of architectural data.

Unfortunately it cannot be said that pyramids have been exhaustively surveyed (we still do not know with certainty the upper slope angles at Dashur). Only at Giza do we have Petrie's precise survey. Converting Petrie's measurements into native units of measure produces a rational plan for the arrangement of Khufu's inner passages and chambers. In addition a definite positional relationship exists between the three large pyramids.

My site is a collection of analyses (citing a number of authors) which have led me to this conclusion. For the most part they should be easily comprehensible (involving the roots of 2, 3, and 5, Pi and Phi) but there are other relations which  lack explanation. So I'm hoping to get some feedback from scientists looking at the purely mathematical aspects of these curious structures. When they get to see them that is.

robin

ps. in the attached image a solution to the layout of the descending passage in Khufu is presented. It derives from the notorious 'circle squared diagram. (All agree that the passage is laid out on the diagonal of the double square. However, beginning with the intersection of the circle and the square 173.2 cubits below base, the axis should emerge 33.6 cubits above pyramid base but the angle of the masonry built section is very slightly less than the rock cut part.) I wrote a short paper on this but I don't know if I am allowed to show it on this website. Please delete if so -

 

 

[exchemist]

54 minutes ago, robincook said:

Dear Swansont,

Ok I'll try to summarize (assuming readers have at least a passing acquaintance with the Giza complex - if not refer to Wikipedia to get up to speed).

Most people today see pyramids as the useless products of a vainglorious elite (albeit at the same time being the focus of popular mysticism). However, if we concentrate on the architectural design of pyramids some surprising relations emerge which are yet to be explained.

Egypt is viewed as a 'craft culture' - assiduously building giant structures in cut stone using the simplest of tools and methods. The Egyptians pushed the limits of what man can achieve using such means. But they were also very meticulous in realizing their designs, and in pyramid complexes we are presented with a large amount of architectural data.

Unfortunately it cannot be said that pyramids have been exhaustively surveyed (we still do not know with certainty the upper slope angles at Dashur). Only at Giza do we have Petrie's precise survey. Converting Petrie's measurements into native units of measure produces a rational plan for the arrangement of Khufu's inner passages and chambers. In addition a definite positional relationship exists between the three large pyramids.

My site is a collection of analyses (citing a number of authors) which have led me to this conclusion. For the most part they should be easily comprehensible (involving the roots of 2, 3, and 5, Pi and Phi) but there are other relations which  lack explanation. So I'm hoping to get some feedback from scientists looking at the purely mathematical aspects of these curious structures. When they get to see them that is.

robin

ps. in the attached image a solution to the layout of the descending passage in Khufu is presented. It derives from the notorious 'circle squared diagram. (All agree that the passage is laid out on the diagonal of the double square. However, beginning with the intersection of the circle and the square 173.2 cubits below base, the axis should emerge 33.6 cubits above pyramid base but the angle of the masonry built section is very slightly less than the rock cut part.) I wrote a short paper on this but I don't know if I am allowed to show it on this website. Please delete if so -

https://independent.academia.edu/robincook

 

As it happens, only today I was reading a very simple explanation for why the base perimeter of the Great Pyramid divided by its height is very close to 2π. It seems the Egyptians may have used a trundle wheel, one cubit in diameter, to measure out the base at 280 revolutions from one corner to the diagonally opposite corner, and then built it 280 cubits high. So they automatically got a ratio involving π, without anyone at the time needing to know anything about it. 

I thought this was rather neat. 

[studiot]

2 hours ago, exchemist said:

As it happens, only today I was reading a very simple explanation for why the base perimeter of the Great Pyramid divided by its height is very close to 2π. It seems the Egyptians may have used a trundle wheel, one cubit in diameter, to measure out the base at 280 revolutions from one corner to the diagonally opposite corner, and then built it 280 cubits high. So they automatically got a ratio involving π, without anyone at the time needing to know anything about it. 

I thought this was rather neat. 

Yes I have seen this before and quoted it here in that long thread about the building of the Pyramids we had a couple of years back.

However the ancient Egyptians knew about Pi

See the Rhind Papyrus (about 1650 BC)

[exchemist]

16 minutes ago, studiot said:

Yes I have seen this before and quoted it here in that long thread about the building of the Pyramids we had a couple of years back.

However the ancient Egyptians knew about Pi

See the Rhind Papyrus (about 1650 BC)

That's interesting.

However that would have been written about a thousand years after the pyramid was built, to judge by the most recent estimates of its age. 

[dimreepr]

32 minutes ago, exchemist said:

That's interesting.

However that would have been written about a thousand years after the pyramid was built, to judge by the most recent estimates of its age. 

does that make it any less interesting?

[zapatos]

23 minutes ago, dimreepr said:

does that make it any less interesting?

I think his point was that it might make it somewhat less pertinent. 

[studiot]

2 hours ago, exchemist said:

However that would have been written about a thousand years after the pyramid was built, to judge by the most recent estimates of its age. 

Yes that paticular papyrus was indeed written about a thousand years after Giza.

Writing and papyrus documents were well known at the time of the building of Giza so any knowledge that was recorded could have been copied forward, just as the knowledge in the scan I posted was transcribed forward over thre and a half thousand years.

I understand not many papyri from antiquity survive and fewer as we go back in time.
Today of course we rely on the hand copying forward onto parchment, for the knowledge of a thousand years ago.

So, although we cannot have proof positive that the Early Dynasties did not know about Pi, we cannot disprove it either.

I omitted the reference my attachment before.

Sorry.

It was from Algebra by Archbold   Pitman 1958

Edited May 23, 2021 by studiot

[robincook]

I think I should mention that many scholars have addressed the question and overwhelmingly Egyptologists believe that the Egyptians did not know Pi. They concede that the Egyptians used a rough approximation for what we call Pi, calculated by squaring 8/9 of a circle, giving a value of 3.16 - sufficient  for estimating the volume of containers - in other words squaring by area. Squaring by circumference is what is usually meant by 'squaring the circle'. The meridian section of Khufu is governed by SEKED  5 cubits 2 palms (in other words height 14 base 11). The fact that these figures produce a value for Pi of 22/7 is considered a coincidence. The whole point of my paper is to demonstrate that, by laying out the descending passage according to the 'circle squared diagram', the pyramid builders were well aware of the concept.

It should be noted that Khufu was also designed using Phi - in the overall design of the pyramid as 356/220 (reducing to the Fibonacci terms 89/55),  and to determine passage junctions within the pyramid. There is also evidence that the same Fibonacci terms were used in pyramid layout.

[studiot]

13 minutes ago, robincook said:

I think I should mention.........

 

13 minutes ago, robincook said:

It should be noted that....................

 

13 minutes ago, robincook said:

There is also evidence........

 

Lots of claims but no supporting evidence or references.

 

More to the point, what is the specific point you wish to discuss or question you wish to ask?

[exchemist]

12 minutes ago, robincook said:

I think I should mention that many scholars have addressed the question and overwhelmingly Egyptologists believe that the Egyptians did not know Pi. They concede that the Egyptians used a rough approximation for what we call Pi, calculated by squaring 8/9 of a circle, giving a value of 3.16 - sufficient  for estimating the volume of containers - in other words squaring by area. Squaring by circumference is what is usually meant by 'squaring the circle'. The meridian section of Khufu is governed by SEKED  5 cubits 2 palms (in other words height 14 base 11). The fact that these figures produce a value for Pi of 22/7 is considered a coincidence. The whole point of my paper is to demonstrate that, by laying out the descending passage according to the 'circle squared diagram', the pyramid builders were well aware of the concept.

It should be noted that Khufu was also designed using Phi - in the overall design of the pyramid as 356/220 (reducing to the Fibonacci terms 89/55),  and to determine passage junctions within the pyramid. There is also evidence that the same Fibonacci terms were used in pyramid layout.

I'm not sure I follow. Are you saying the Egyptians didn't know π  but the builders of the pyramid (I presume you mean the designers) did? Are you then claiming the builders or designers were not Egyptian, but brought in from somewhere else? 

[robincook]

21 hours ago, studiot said:

 

 

 

Lots of claims but no supporting evidence or references.

 

More to the point, what is the specific point you wish to discuss or question you wish to ask?

Hello Studiot,

Supporting evidence and references are listed on my website.  The essential survey data to back up the claim for Pi and Phi in Khufu is that provided by Petrie, available on the net here -

http://www.ronaldbirdsall.com/gizeh/petrie/index.htm

As to my point - many see pyramids as useless piles of stone constructed to massage  the egos of vainglorious kings. Others imbue the pyramids with all kinds of mysticism. However, by looking at the survey data for the Giza group, interesting positional relations appear and these need to be explained, whatever one's point of view. So my first step is to present the data, such as it is.

Once this data has been assimilated one must ask what does it all mean? My tentative conclusion is that at the height of Egypt's prosperity (that is during the reigns of Sneferu and Khufu) a mathematically inclined priesthood had for a moment gained power - although it was not to last because of climate change towards the end of the IVth dynasty; the state became poorer and subsequent pyramids were smaller, more shoddily built, and lacking the kind of geometry we see at Giza.

Perhaps this is the wrong section to  have put my post but at Giza we seem to be dealing with a mathematical philosophy. It had been my hope that, after assimilating the data, there would be something to discuss.

robin

 

On 5/23/2021 at 4:52 PM, exchemist said:

As it happens, only today I was reading a very simple explanation for why the base perimeter of the Great Pyramid divided by its height is very close to 2π. It seems the Egyptians may have used a trundle wheel, one cubit in diameter, to measure out the base at 280 revolutions from one corner to the diagonally opposite corner, and then built it 280 cubits high. So they automatically got a ratio involving π, without anyone at the time needing to know anything about it. 

I thought this was rather neat. 

This idea was promoted by Mendelssohn about 40 years ago, but pyramids have cores cut into steps so no go. Besides only three pyramids have the 'Pi slope'.

23 hours ago, exchemist said:

I'm not sure I follow. Are you saying the Egyptians didn't know π  but the builders of the pyramid (I presume you mean the designers) did? Are you then claiming the builders or designers were not Egyptian, but brought in from somewhere else? 

No. The designers were Egyptian.  The question is what metaphysical significance they attributed to their geometric conceits.

[swansont]

1 hour ago, robincook said:

Supporting evidence and references are listed on my website. 

!

Moderator Note

Which, as you have been told, is insufficient. Our rules require you post the information here.

If you can’t or won’t follow the rules, the thread will be closed 

 

1 hour ago, robincook said:

 

This idea was promoted by Mendelssohn about 40 years ago, but pyramids have cores cut into steps so no go. Besides only three pyramids have the 'Pi slope'.

No. The designers were Egyptian.  The question is what metaphysical significance they attributed to their geometric conceits.

Didn’t you just deny there were geometric conceits in the previous sentence? 

[exchemist]

3 hours ago, robincook said:

Hello Studiot,

Supporting evidence and references are listed on my website.  The essential survey data to back up the claim for Pi and Phi in Khufu is that provided by Petrie, available on the net here -

http://www.ronaldbirdsall.com/gizeh/petrie/index.htm

As to my point - many see pyramids as useless piles of stone constructed to massage  the egos of vainglorious kings. Others imbue the pyramids with all kinds of mysticism. However, by looking at the survey data for the Giza group, interesting positional relations appear and these need to be explained, whatever one's point of view. So my first step is to present the data, such as it is.

Once this data has been assimilated one must ask what does it all mean? My tentative conclusion is that at the height of Egypt's prosperity (that is during the reigns of Sneferu and Khufu) a mathematically inclined priesthood had for a moment gained power - although it was not to last because of climate change towards the end of the IVth dynasty; the state became poorer and subsequent pyramids were smaller, more shoddily built, and lacking the kind of geometry we see at Giza.

Perhaps this is the wrong section to  have put my post but at Giza we seem to be dealing with a mathematical philosophy. It had been my hope that, after assimilating the data, there would be something to discuss.

robin

 

This idea was promoted by Mendelssohn about 40 years ago, but pyramids have cores cut into steps so no go. Besides only three pyramids have the 'Pi slope'.

No. The designers were Egyptian.  The question is what metaphysical significance they attributed to their geometric conceits.

So, let me understand this. The Egyptians, so you say, did not know π, but the pyramids builders who, you say, were Egyptians, did. How does that work?

Do you mean that while most of Egyptian society didn't, this hypothetical priestly caste of yours did? 

 

Also, you'll have to explain to me why the cutting of the pyramid core into steps precludes them making it 280 cubits high by design. 

Edited May 25, 2021 by exchemist

[robincook]

18 hours ago, swansont said:

!

Moderator Note

Which, as you have been told, is insufficient. Our rules require you post the information here.

If you can’t or won’t follow the rules, the thread will be closed 

 

Didn’t you just deny there were geometric conceits in the previous sentence? 

sorry swansont, what previous sentence is that?

[SergUpstart]

On 5/8/2021 at 5:54 PM, robincook said:

I hope it's ok to post in the general philosophy section - I don't know which would be a better section to post in.

It would be nice if a section "History and Archeology" was created on the forum

[robincook]

17 hours ago, exchemist said:

So, let me understand this. The Egyptians, so you say, did not know π, but the pyramids builders who, you say, were Egyptians, did. How does that work?

Do you mean that while most of Egyptian society didn't, this hypothetical priestly caste of yours did? 

 

Also, you'll have to explain to me why the cutting of the pyramid core into steps precludes them making it 280 cubits high by design. 

hi exchemist,

You seem to be making a mountain out of a molehill - the Giza pyramids were designed and built by native Egyptians over a span of years from about 2580 BC to 2500 BC. Of course the height of Khufu was made 280 cubits by design. The fact that the builders saved a great deal of work and stone by terracing the rocky knoll over which Khufu was built is irrelevant. I wonder why you think that cutting steps precludes the builders from designing whatever they wanted? What have I written that gives you this idea?

Egyptologists maintain that the pyramid architects did not know Pi. The value of Pi 22/7 found in Khufu is thought to be coincidental. However I found that the descending passage of Khufu (probably the first element to be created at Giza) appears to have been laid out according to the circle squared scheme. (But if you can find a better explanation for the passage layout I'd love to hear it.) This suggests that the architects did 'know Pi' but had little  interest in calculating more precise values, as Mesopotamians did.  Lightbody has proposed that the circle was viewed as a symbol of 'protection' . Actually that is the reason for posting in this philosophy forum - now that Khufu has been analyzed what did this geometry mean to the architects? Why design a pyramid on the basis of Pi and Phi?

The vast majority of Egyptians could neither read or write and were highly superstitious. Of course they were aware of the tomb narrative, could witness for themselves the rising, culmination, and setting of their star gods in the sky; the intervisibility of pyramid sites across the Nile and the positioning of pyramid sites to correspond to the setting of prominent Decanal stars. But when they were drafted to build pyramids they had no way of appreciating the sophisticated design upon which they were working. So yes, the design of Khufu must be attributed to a priestly caste. (Unless you believe kings were capable of designing pyramids 😉

 

[Alex_Krycek]

On 5/23/2021 at 10:55 PM, studiot said:

Yes I have seen this before and quoted it here in that long thread about the building of the Pyramids we had a couple of years back.

However the ancient Egyptians knew about Pi

See the Rhind Papyrus (about 1650 BC)

What text is this from? (source)

[exchemist]

44 minutes ago, robincook said:

hi exchemist,

You seem to be making a mountain out of a molehill - the Giza pyramids were designed and built by native Egyptians over a span of years from about 2580 BC to 2500 BC. Of course the height of Khufu was made 280 cubits by design. The fact that the builders saved a great deal of work and stone by terracing the rocky knoll over which Khufu was built is irrelevant. I wonder why you think that cutting steps precludes the builders from designing whatever they wanted? What have I written that gives you this idea?

Egyptologists maintain that the pyramid architects did not know Pi. The value of Pi 22/7 found in Khufu is thought to be coincidental. However I found that the descending passage of Khufu (probably the first element to be created at Giza) appears to have been laid out according to the circle squared scheme. (But if you can find a better explanation for the passage layout I'd love to hear it.) This suggests that the architects did 'know Pi' but had little  interest in calculating more precise values, as Mesopotamians did.  Lightbody has proposed that the circle was viewed as a symbol of 'protection' . Actually that is the reason for posting in this philosophy forum - now that Khufu has been analyzed what did this geometry mean to the architects? Why design a pyramid on the basis of Pi and Phi?

The vast majority of Egyptians could neither read or write and were highly superstitious. Of course they were aware of the tomb narrative, could witness for themselves the rising, culmination, and setting of their star gods in the sky; the intervisibility of pyramid sites across the Nile and the positioning of pyramid sites to correspond to the setting of prominent Decanal stars. But when they were drafted to build pyramids they had no way of appreciating the sophisticated design upon which they were working. So yes, the design of Khufu must be attributed to a priestly caste. (Unless you believe kings were capable of designing pyramids 😉

 

OK, so you maintain they did know π, contrary to what most Egyptologists say. That's fine, I just wasn't clear what you were saying earlier.

[swansont]

2 hours ago, robincook said:

sorry swansont, what previous sentence is that?

Only three pyramids had the pi slope. 

[studiot]

48 minutes ago, Alex_Krycek said:

What text is this from? (source)

 

Actually I did give the reference in my immediately following post.

On 5/23/2021 at 7:21 PM, studiot said:

I omitted the reference my attachment before.

Sorry.

It was from Algebra by Archbold   Pitman 1958

 

1 hour ago, robincook said:

The vast majority of Egyptians could neither read or write and were highly superstitious. Of course they were aware of the tomb narrative, could witness for themselves the rising, culmination, and setting of their star gods in the sky; the intervisibility of pyramid sites across the Nile and the positioning of pyramid sites to correspond to the setting of prominent Decanal stars. But when they were drafted to build pyramids they had no way of appreciating the sophisticated design upon which they were working. So yes, the design of Khufu must be attributed to a priestly caste. (Unless you believe kings were capable of designing pyramids

Yes I think this is a pretty fair summary although it should be recognised that ancient egyptian civilisation and culture spanned many centuries (rather more than our own) so to say that they did or did not know Pi you would also need to specify a time period.

However I have already asked for proper substantiating references to this extraordinary claim and a moderator has pointed out the rules here over this forum requirement.

1 hour ago, robincook said:

Egyptologists maintain that the pyramid architects did not know Pi.

Over the rather fewer centuries of our civilisation there have been many investigations of the egyptian pyramids, rather fewer comparisons with pyramids in other parts of the world, and many 'egyptologists' and hypotheses, including attempts by modern engineers to recreate ancient building techniques etc.

So I ask you again which egyptologists ?

 

1 hour ago, robincook said:

The fact that the builders saved a great deal of work and stone by terracing the rocky knoll over which Khufu was built is irrelevant.

I find this comment at direct variance with cladking's long thread on the construction of the pyramids.

In deference to Alex, I will refer to this thread.

https://www.scienceforums.net/topic/85760-soft-science-and-evidence-of-your-own-eyes/#comments

 

1 hour ago, robincook said:

appears to have been laid out according to the circle squared scheme.

I assume this is a further reference to the diagram you originally posted withhout any explanation, and later perhaps referrred to as a double or two square.

Again can we have some proper explanation please ?

Edited May 26, 2021 by studiot

[SergUpstart]

I recommend watching a great movie about the pyramids " revelations of the pyramids" 

What is interesting to pay attention to. Pyramids are not tetrahedra. At their base is an octagon, so that on the days of the equinox at sunrise, half of the faces of the pyramids are illuminated and the other half remains in shadow.

And now about choosing a place to build pyramids. The film says that if you build a straight line from Giza at an angle of 30 degrees to the parallel, then the idols from Easter Island and Machu Picchu will be on this straight line. And the Mayan pyramids are on the same parallel as Giza.

I wanted to see what was on the same meridian as Giza. And it turned out that if you go from Giza to the North, you will pass through the capital of the Byzantine and later Ottoman Empire, Constantinople (Istanbul), then through the capital of Kievan Rus, Kiev, the capital of Novgorod Rus, Novgorod, and finally come to the capital of the Russian Romanov Empire, St. Petersburg.

[studiot]

33 minutes ago, SergUpstart said:

And now about choosing a place to build pyramids. The film says that if you build a straight line from Giza at an angle of 30 degrees to the parallel, then the idols from Easter Island and Machu Picchu will be on this straight line. And the Mayan pyramids are on the same parallel as Giza.

I wanted to see what was on the same meridian as Giza. And it turned out that if you go from Giza to the North, you will pass through the capital of the Byzantine and later Ottoman Empire, Constantinople (Istanbul), then through the capital of Kievan Rus, Kiev, the capital of Novgorod Rus, Novgorod, and finally come to the capital of the Russian Romanov Empire, St. Petersburg.

 

Please not more Ley Lines voodoo and rubbish.

Those points alone remove any validity that video might offer.

[exchemist]

1 hour ago, SergUpstart said:

I recommend watching a great movie about the pyramids " revelations of the pyramids" 

What is interesting to pay attention to. Pyramids are not tetrahedra. At their base is an octagon, so that on the days of the equinox at sunrise, half of the faces of the pyramids are illuminated and the other half remains in shadow.

And now about choosing a place to build pyramids. The film says that if you build a straight line from Giza at an angle of 30 degrees to the parallel, then the idols from Easter Island and Machu Picchu will be on this straight line. And the Mayan pyramids are on the same parallel as Giza.

I wanted to see what was on the same meridian as Giza. And it turned out that if you go from Giza to the North, you will pass through the capital of the Byzantine and later Ottoman Empire, Constantinople (Istanbul), then through the capital of Kievan Rus, Kiev, the capital of Novgorod Rus, Novgorod, and finally come to the capital of the Russian Romanov Empire, St. Petersburg.

Well of course they are not tetrahedra. They have a square base.So like any square pyramid they have 5 sides. A tetrahedron has a triangular base.

But this film is worthless. I quote Wikipedia: "The Revelation of the Pyramids (French: La révélation des pyramides) is a conspiracy theory pseudo-scientific documentary directed by Patrice Pooyard and released in 2010."

Edited May 26, 2021 by exchemist