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Ozymandias

The Great Pyramid (G1)

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Ozymandias
Posted (edited)

Not wanting to hijack another related thread, and not being an Egyptologist, I have a very practical problem in mind. 

Imagine you are the guy who pegged or marked out the base of the Great Pyramid on its green-field site at Giza over 5000 years ago. How was it done? Using what equipment and knowledge?

As far as I know the Egyptians could not compute square roots and had not developed any trigonometry. They may have known Pythagoras' Theorem and used the 3 : 4 : 5 triangle (the Builder's Square) to lay out a right-angle (90°) but, if so, why is the base of the Great Pyramid not a perfect square.

Just how did they lay that base out in practice?

Edited by Ozymandias

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Sir Wearer of Hats

I seem to recall a documentary I saw about it, it was all string and stakes.

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stereologist

I think that people could have used ropes to lay out a base. Ropes do stretch and they do change length due to humidity. That is why chains are used today. In the trans-India survey the chains were used under shade to avoid thermal issues.

Maybe they used one rope to establish a side length and a second rope to verify that the diagonals were the same length. Trial and error could be used to get the base pretty close to a square.

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bison
2 hours ago, Ozymandias said:

Not wanting to hijack another related thread, and not being an Egyptologist, I have a very practical problem in mind. 

Imagine you are the guy who pegged or marked out the base of the Great Pyramid on its green-field site at Giza over 5000 years ago. How was it done? Using what equipment and knowledge?

As far as I know the Egyptians could not compute square roots and had not developed any trigonometry. They may have known Pythagoras' Theorem and used the 3 : 4 : 5 triangle (the Builder's Square) to lay out a right-angle (90°) but, if so, why is the base of the Great Pyramid not a perfect square.

Just how did they lay that base out in practice?

I found this brief summary of ancient Egyptian surveying tools and techniques:

http://www.surveyhistory.org/egyptian_surveying_tools1.htm

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Advenix
2 hours ago, bison said:

  For a building made nearly 5000 years ago, that appears excellent. Probably not excellent enough, though, to support the idea that the Great Pyramid was built by, or with the aid of advanced extraterrestrials, as some would have it.   

To be sure of the tiny error, one must go back in time and do the survey upon the completion of the pyramid, because over the long millennia the pyramid has eroded with plenty of the baseline stones being taken away for other building purposes. That's, of course, isn't possible, but one can deduce it...

The Dash Foundation’s study shows for the first time that the base of the Great Pyramid isn’t a perfect square: its west side is very slightly longer than its east side.
http://nationalpost.com/news/world/yes-a-new-study-reveals-the-great-pyramid-of-giza-isnt-a-perfect-square-but-its-still-a-structural-marvel

 According to the Spielberg movie Close Encounters of the Third Kind, the ET's started to communicate with earthlings by playing musical tones. The same happened when the Head of the Imperial Surveyor Team stood on the site where the Great Pyramid of Giza was to be erected. All of a sudden, a celestial vehicle showed above and a single, long lasting tone was heard. Since the Latin letter that resembles a pyramid the most is letter A, and note A is a standard tuning pitch equaling 440 Hz, the Imperial Architect decided that the base of the Great Pyramid would measure 440 Egyptian Royal cubits, as suggested by the "gods."

But what could the Egyptians possibly know about Western music?

Well, the celestial vehicle developed a gravity stabilizer problem and crash landed. When the Egyptians entered the crippled craft, they found a strange human-like creature attempting to recover the Futurolog, which is a long list of future events. It was written in hieroglyphs and some other language, which is now recognized as English.

That's why the Egyptian builders decided that the west baseline would be longer to remind the Ph.D.s of Western music in case they would decide to ponder the deviation from the perfect.
https://www.youtube.com/watch?v=m2JL0xABlrQ
https://www.youtube.com/watch?v=5_JWMtPVf-A

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jaylemurph
Posted (edited)

Actually, we don't need to deduce it. It's a matter of historical record the Giza pyramids were encased in limestone. That would have changed the metrics of the baseline, but you haven't included that in your mathturbation at all, have you?

--Jaylemurph

Edited by jaylemurph
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kmt_sesh
2 minutes ago, jaylemurph said:

Actually, we don't need to deduce it. It's a matter of historical record the Giza pyramids were encased in limestone. That would have changed the metrics of the baseline, but you haven't included that in your mathturbation at all, have you?

--Jaylemurph

I'm struggling to determine if what he wrote is meant to be taken seriously.

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kmt_sesh
1 hour ago, bison said:

I found this brief summary of ancient Egyptian surveying tools and techniques:

http://www.surveyhistory.org/egyptian_surveying_tools1.htm

I like this link. The information is good. The ancient tools were simple by our standards, but were more than capable for the job. Stretching a rope graduated with knots was a simple way to establish a base; they had plumbs, levels, and right angles to do their work. There was even a ritual component in which Seshat, the goddess of measurements, played an important part in a ceremony called "Stretching the Cord."

Aliens were neither there nor needed. For one thing, there is no such thing as aliens visiting earth, and for another, the ancient Egyptians were smart enough to figure it out on their own.

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Advenix
33 minutes ago, jaylemurph said:

Actually, we don't need to deduce it. It's a matter of historical record the Giza pyramids were encased in limestone. That would have changed the metrics of the baseline, but you haven't included that in your mathturbation at all, have you?

--Jaylemurph

The dimensions of a product delivered by a manufacturer inside a box are not affected by the dimension of the box - you should know that. Most of the encasing stones fell off during the earthquake of 1303 AD, which is the most likely cause of other dimensional discrepancies.

You would never solve the puzzle, which specific object letter A represents, because you would never notice the shape of the letter, use the clue A=440Hz, replace Hz with cubits to get you to the base of the Great Pyramid of Giza. Specifically to its western, disputed side via Western music and its standard pitch. That's why you will never ever solve any puzzle written by history.

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kmt_sesh

The origin of the Western letter A is well understood and has  been for a very long time. There is no reason to invent some sci-fi scenario. See below:

First-Alphabets1.jpg

The ox head at top-left is from Egyptian hieroglyphs and was borrowed by Canaanites for their Proto-Sinaitic script even before the Phoenicians came along.

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Advenix
Posted (edited)
36 minutes ago, kmt_sesh said:

I like this link. The information is good. The ancient tools were simple by our standards, but were more than capable for the job. Stretching a rope graduated with knots was a simple way to establish a base; they had plumbs, levels, and right angles to do their work. There was even a ritual component in which Seshat, the goddess of measurements, played an important part in a ceremony called "Stretching the Cord."

Aliens were neither there nor needed. For one thing, there is no such thing as aliens visiting earth, and for another, the ancient Egyptians were smart enough to figure it out on their own.

The ancients of Egypt acquired Wisdom in the year 2950 BC, which became the Supreme Year of the Bronze Age. That's why their civilization became very notable to the modern age Man only after that year.

Edited by Advenix
typo
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kmt_sesh

So, some 400 years before they got around to erecting their greatest monument of the Old Kingdom? Boy, they sure took their sweet time.

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cormac mac airt

Well, I guess if Close Encounters of the Third Kind is a documentary then Stargate SG-1 must be too. When did the Goa’uld land in Egypt? :lol:

cormac

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kmt_sesh
1 minute ago, cormac mac airt said:

Well, I guess if Close Encounters of the Third Kind is a documentary then Stargate SG-1 must be too. When did the Goa’uld land in Egypt? :lol:

cormac

Now, you and I know never to doubt Stargate. As Teal'c would say, "Indeed."

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danydandan
3 hours ago, Advenix said:

To be sure of the tiny error, one must go back in time and do the survey upon the completion of the pyramid, because over the long millennia the pyramid has eroded with plenty of the baseline stones being taken away for other building purposes. That's, of course, isn't possible, but one can deduce it...

The Dash Foundation’s study shows for the first time that the base of the Great Pyramid isn’t a perfect square: its west side is very slightly longer than its east side.
http://nationalpost.com/news/world/yes-a-new-study-reveals-the-great-pyramid-of-giza-isnt-a-perfect-square-but-its-still-a-structural-marvel

 According to the Spielberg movie Close Encounters of the Third Kind, the ET's started to communicate with earthlings by playing musical tones. The same happened when the Head of the Imperial Surveyor Team stood on the site where the Great Pyramid of Giza was to be erected. All of a sudden, a celestial vehicle showed above and a single, long lasting tone was heard. Since the Latin letter that resembles a pyramid the most is letter A, and note A is a standard tuning pitch equaling 440 Hz, the Imperial Architect decided that the base of the Great Pyramid would measure 440 Egyptian Royal cubits, as suggested by the "gods."

But what could the Egyptians possibly know about Western music?

Well, the celestial vehicle developed a gravity stabilizer problem and crash landed. When the Egyptians entered the crippled craft, they found a strange human-like creature attempting to recover the Futurolog, which is a long list of future events. It was written in hieroglyphs and some other language, which is now recognized as English.

That's why the Egyptian builders decided that the west baseline would be longer to remind the Ph.D.s of Western music in case they would decide to ponder the deviation from the perfect.
https://www.youtube.com/watch?v=m2JL0xABlrQ
https://www.youtube.com/watch?v=5_JWMtPVf-A

The frequency for A ranges from 432 to 446. The average of this is 439 which still isn't 440.

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Ozymandias

It would seem reasonable to speculate that they used ropes (made of what material?) or rods to measure out lengths on the ground. Is their evidence of this?

But, more importantly, what method did they use to lay out a 90° angle on the ground? Did they effectively understand Pythagoras Theorem? 

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danydandan
Posted (edited)
36 minutes ago, Ozymandias said:

It would seem reasonable to speculate that they used ropes (made of what material?) or rods to measure out lengths on the ground. Is their evidence of this?

But, more importantly, what method did they use to lay out a 90° angle on the ground? Did they effectively understand Pythagoras Theorem? 

I suppose them ropes are long gone. But you could also assume they used ropes as measurement tools also. There are cubit rods from AE.

Regarding the 90 degree angle, if I may quote Harte,

"The AE's knew the square root of 3 indirectly. Same with the square root of two.

If you make a diagonal in a rectangle twice as long as the short side of the rectangle, the rectangle's long side is equal to the square root of 3, taking the short side as one.

Also, for a one by one square, the diagonal is equal to the square root of 2.

Pi and phi they didn't know, but they probably knew how to construct the "golden rectangle." You can do it with compass and straightedge (two strings and some stakes.) Takes about three steps.

Harte"

They may have used that methodology, I don't know. It's obvious they had a grasp of trigonometry anyways.. I wonder if they grasped three dimensional trigonometry?

Edited by danydandan
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Tom the Photon
3 hours ago, Advenix said:

The ancients of Egypt acquired Wisdom in the year 2950 BC, which became the Supreme Year of the Bronze Age. That's why their civilization became very notable to the modern age Man only after that year.

On March 15th, at 3.22 pm.  That's the exact moment Pythagoras' great-grandad invented the letter "M".  Before that they only had Wisdo, which was silly.

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seanjo
39 minutes ago, Ozymandias said:

It would seem reasonable to speculate that they used ropes (made of what material?) or rods to measure out lengths on the ground. Is their evidence of this?

But, more importantly, what method did they use to lay out a 90° angle on the ground? Did they effectively understand Pythagoras Theorem? 

They knew about Isosceles triangle's and they had set squares and plumbobs.

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Tom the Photon
30 minutes ago, Ozymandias said:

It would seem reasonable to speculate that they used ropes (made of what material?) or rods to measure out lengths on the ground. Is their evidence of this?

But, more importantly, what method did they use to lay out a 90° angle on the ground? Did they effectively understand Pythagoras Theorem? 

I find it quite easy to imagine ancient peoples spotting patterns in stacked bricks or stones, and some bright spark having the imagination to measure a few diagonals (I can't spell hypotenuses).  After spotting 3-4-5 and 5-12-13 they would have been able to put these numbers to use, even if they couldn't explain precisely why it happens.

I remember reading somewhere that they first dug channels filled with water to find a level across the plateau.  Is there any truth in this / evidence?  It was a children's guide to AE and made it look really easy!

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danydandan
11 minutes ago, seanjo said:

Didn't know they used fractions, that's interesting thanks.

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Ozymandias
3 hours ago, danydandan said:

I suppose them ropes are long gone. But you could also assume they used ropes as measurement tools also. There are cubit rods from AE.

Regarding the 90 degree angle, if I may quote Harte,

"The AE's knew the square root of 3 indirectly. Same with the square root of two.

If you make a diagonal in a rectangle twice as long as the short side of the rectangle, the rectangle's long side is equal to the square root of 3, taking the short side as one.

Also, for a one by one square, the diagonal is equal to the square root of 2.

Pi and phi they didn't know, but they probably knew how to construct the "golden rectangle." You can do it with compass and straightedge (two strings and some stakes.) Takes about three steps.

Harte"

They may have used that methodology, I don't know. It's obvious they had a grasp of trigonometry anyways.. I wonder if they grasped three dimensional trigonometry?

The AE knew about congruent triangles and ratio and proportion. They had techniques for making indirect measurements using similar triangles but they did not know trigonometry as we do. As far as I can see they were in a pre-trigonometric phase of development.

'The AE's knew the square root of 3 indirectly' - what does this mean exactly? Being able to draw or lay out a right-angled triangle does not mean they understood Pythagoras Theorem, although they may well have done. The mathematics of the relationship between the sides of the 'Builder's Square' (3 : 4 : 5 triangle) is easily explained using pure geometry: 3^2 + 4^2 = 5^2, that is, 3x3 + 4x4 = 5x5. But these are all integral (whole number) values and I think the AEs knew about Pythaogrean triples and how to calculate.  However, I don't believe they had a way of writing or evaluating the square root of 2 or the square root of three even though these numbers arise from the the geometry of right-angled triangles: that is, from the 1 : 1 : sqrt2 and the 1 : 2 : sqrt3 triangles.

So, if they could lay out the rectangular square of the base of the Great Pyramid on the ground using a 3 : 4 : 5 triangle that does not mean they understood that sqrt2 = 1.4142.. or that sqrt3 = 1.732.... In fact, they could not write decimal number and routinely treated decimal fraction of whole numbers as a series of repeated or embedded fractions. 

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danydandan
6 minutes ago, Ozymandias said:

The AE knew about congruent triangles and ratio and proportion. They had techniques for making indirect measurements using similar triangles but they did not know trigonometry as we do. As far as I can see they were in a pre-trigonometric phase of development.

'The AE's knew the square root of 3 indirectly' - what does this mean exactly? Being able to draw or lay out a right-angled triangle does not mean they understood Pythagoras Theorem, although they may well have done. The mathematics of the relationship between the sides of the 'Builder's Square' (3 : 4 : 5 triangle) is easily explained using pure geometry: 3^2 + 4^2 = 5^2, that is, 3x3 + 4x4 = 5x5. But these are all integral (whole number) values and I think the AEs knew about Pythaogrean triples and how to calculate.  However, I don't believe they had a way of writing or evaluating the square root of 2 or the square root of three even though these numbers arise from the the geometry of right-angled triangles: that is, from the 1 : 1 : sqrt2 and the 1 : 2 : sqrt3 triangles.

So, if they could lay out the rectangular square of the base of the Great Pyramid on the ground using a 3 : 4 : 5 triangle that does not mean they understood that sqrt2 = 1.4142.. or that sqrt3 = 1.732.... In fact, they could not write decimal number and routinely treated decimal fraction of whole numbers as a series of repeated or embedded fractions. 

What I assume Harte meant was that they understood the relationships of the lenghts of each side and the angle. Not thst they knew the actual measurement of the square roots.

I keep seeing conflicting information regarding their use of fractions, is there a definitive answer to their use of fractions. I am new to the ancient Egyptian history. Usually confined myself to religious, Celtic and pre world war European history.

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