Giza Pyramid Height Relationships

[Bennu]

There is no mystery, the aim was that G3 was just as high as G1 having less space to build it on, so it was build higher in the valley to an altitude where its silhouette made it look just as tall as Khufu's.

Don't you guys familiarize yourself with the area before you start m@sturb@ting your brains?

Seems awfully simplistic to me. I don't think it looks as tall as G1 no matter how you look at it really.

[questionmark]

Seems awfully simplistic to me. I don't think it looks as tall as G1 no matter how you look at it really.

We are talking about the beginning of the bronze age here, a little more than 500 years before they still were using stone spears. It was simple.

Edited August 13, 2014 by questionmark

[Bennu]

The most obvious flaw in your method is that half of G3 width is not 98.98 cubits. The full side lengths would then be 191.9 cubits when Petrie reports a mean length of 201.435 cubits (4153.6 inches). The difference is more than 9 cubits, more than 16 feet. If you use the real G3 half side length, the height with your procedure comes out to 162.914819 cubits. That's way over the true height.

It also produces a height for G2 of 272.708247 cubits. That seems to be a little short. I admit it's very close though. However that would make a slope of 53.0000542° and none of the readings taken by Petrie on the remaining casing stones are that low.

What you have here is a classic case of "close but no cigar".

In that post the height of G3 produced by that method should be 128.12421 cubits rather than 162.914819 cubits. It's still over by 3 cubits, about 5 feet. The method does work surprisingly well for the GP itself though, I'll give it that much, though it doesn't produce the true GP slope angle. For it to work with G3 that pyramid would have to have the same slope angle, which it does not. The slope produced is 51° 49' 38.25, which matches neither pyramid precisely.

Edited August 13, 2014 by Bennu

[Bennu]

We care talking about the beginning of the bronze age here, a little more than 500 years before they still were using stone spears. It was simple.

You think the Giza pyramids are "simple", huh? Wow.

[questionmark]

You think the Giza pyramids are "simple", huh? Wow.

Yes, there is nothing exceptional, brain wrecking or highly precise about it. It was just a lot of work.

And I admire the ancient Egyptians for getting it together. Any more advanced civilization than them would fast loose my respect given the blundering, ill fitting and tons of mortar used to put the thing up.

[jaylemurph]

Simply stating an obvious fact. I'm not trying to brag about it. You made a statement ("...you mean besides the opportunity for Bennu to be one person in history to truly unlock the Secrets of the Pyramids™?") and I had to agree that it was appropriate. Then I simply added "until then, looks like I have the only explanation, therefore the best one available".

You certainly don't have the /only/ explanation. You have /an/ explanation, and one that can't even generate consensus here, let alone amongst professionals and academics. The fact that you apparently can't even concede of other explanations -- or the fact that there might not be a tenable, logical explanation -- is pretty staggeringly arrogant.

The fact that this "explanation" will almost certainly never leave the confines of wherever you post it on the internet is a pretty fitting reward for that, though.

--Jaylemurph

[Bennu]

Yes, there is nothing exceptional, brain wrecking or highly precise about it. It was just a lot of work.

And I admire the ancient Egyptians for getting it together. Any more advanced civilization than them would fast loose my respect given the blundering, ill fitting and tons of mortar used to put the thing up.

I believe the spelling should be "lose", not "loose", which is the opposite of tight.

Edited August 13, 2014 by Bennu

[Bennu]

You certainly don't have the /only/ explanation. You have /an/ explanation, and one that can't even generate consensus here, let alone amongst professionals and academics. The fact that you apparently can't even concede of other explanations -- or the fact that there might not be a tenable, logical explanation -- is pretty staggeringly arrogant.

The fact that this "explanation" will almost certainly never leave the confines of wherever you post it on the internet is a pretty fitting reward for that, though.

--Jaylemurph

I was not aware of any other published explanations when I wrote that. I still don't know of any that actually check out and are something other than extremely feeble, like that G3 magically appears as high as G1. Sure, if you stand right in front of it with G1 directly behind it. Otherwise, nope. And if that was how they intended to make it look as high as G1 then they could have made it a whole lot smaller than it is. So it still doesn't explain the precise height. Where's the magic spot that you have to stand for it to look as big as G1 anyway? Is there a marking saying "stand here"?

This part is based on nothing I know of; "The fact that you apparently can't even concede of other explanations -- or the fact that there might not be a tenable, logical explanation". I can not only concede of other explanation but I can even conceive of other explanations. I find it unlikely that there is no explanation at all. Nothing about Giza looks arbitrary to me.

Edited August 13, 2014 by Bennu

[kmt_sesh]

Pyramid measurements do not interest me terribly, but what seems clear in much of Dynasty 4 is one king's desire to make his burial monument greater than the previous king's. Sneferu outdid himself a couple of times and Khufu established the standard at Giza, As far as that goes, the transition from Khufu (G1) to Khafre (G2) does not represent a straight order of kings. How does Djedefre fit in at Abu Rawash? It was not of the same stuff as the Giza pyramids but was at a much higher elevation than Giza. Then there's the unfinished pyramid at Zawiyet el Aryan by an ephemeral king named Seth?ka; the growing consensus is now that this otherwise unknown king followed Djedefre.

Only with Khafre do we see a return to Giza. I think a grand, unified, uninterrupted plan for Giza does not survive scrutiny. And how does the height theory factor in the lessening socioeconomic status toward the end of Dynasty 4, culminating not in a pyramid at all but a huge mastaba for Shepseskaf?

With respect, do you think you've discovered something all historians and Egyptologists have missed over the past 250 years, or discovered another way to look at the Giza pyramids mathematically? I'm an admitted dimwit when it comes to math, but when it comes to Giza, people of all sorts love playing with the numbers.

[Golden Duck]

Do I have to solve ALL the mysteries myself? I showed that G3 height is G1 height divided by sqrt 5. The mystery is how it was carried out. It's like the case of how the GP was built so precisely and with such large stones. Nobody knows, it's a mystery. I showed that the sqrt 5 height ratio was carried out in the real world, as evidenced by the pyramids themselves. You have to figure out how it came to be. You can say it's just coincidence but who would really believe that, especially when the Giza rectangle has sides of sqrt 2 and sqrt 3 x 1000? I guess that's all just coincidence too, huh?

Yeah man, coincidences can't happen...

• Light travels at approximately 300,000,000 m/s.
  
• There average distance from the pole to the equator is 10,000 metres.
  
• Light will travel the distance of this arc 30 times in one second.
  
• The prime factors of 30 are 2, 3 and 5.
  
• The sum of 2, 3 and 5 is 9.
  
• The are nine deities in the Ennead.
  

This is all too much of a coincidence. The Earth's size is the design of Ancient Aliens, right?

[Bennu]

With respect, do you think you've discovered something all historians and Egyptologists have missed over the past 250 years, or discovered another way to look at the Giza pyramids mathematically?

Yes, on both counts. I suppose it's possible that somebody noticed it before but never reported it publicly. It's weird really. When I found that dividing G1 height by G3 height produced sqrt 5, I expected to find that it had been noticed and reported long ago. Imagine my surprise when I couldn't find any other mention of it on the web at all. In fact, even now if you do a search on Google about it you'll only find it mentioned on two forums and nowhere else, and both of those forum threads were made by me under other user names in 2007. My theory about how G2 height was derived by a 1:5 rectangle didn't exist at that time though. I had a different theory about G2 at that time. It still could be the correct one. I'm my own competition.

Edited August 14, 2014 by Bennu

[stereologist]

Do I have to solve ALL the mysteries myself? I showed that G3 height is G1 height divided by sqrt 5. The mystery is how it was carried out. It's like the case of how the GP was built so precisely and with such large stones. Nobody knows, it's a mystery. I showed that the sqrt 5 height ratio was carried out in the real world, as evidenced by the pyramids themselves. You have to figure out how it came to be. You can say it's just coincidence but who would really believe that, especially when the Giza rectangle has sides of sqrt 2 and sqrt 3 x 1000? I guess that's all just coincidence too, huh?

You have not shown that the ratio is the square root of 5. What you have shown is that the ratio is approximately the square root of 5. You seem to think that square roots are special. Is there anything important in them? The answer to that depends on the context. In this case I see nothing special since you can't show a reason for it. In this context then, the square root of anything is of no interest.

When you laid out the construction you purposely tried to introduce the square root of 5 and did it in a rather bizarre way. You did it with no purpose other than to introduce the square root of 5. Consider the Egyptians. They don't know the Pythagorean theorem. They don't know about irrational numbers. They don't know about decimal expressions. Yet, you think that people completely unaware of any of this are going to consider the square root of 5 of interest.

What you need to do is to create a geometrical construction that introduces the square root of 5. That is what I originally meant. Figure out a construction which reduces the size of the the pyramid and leaves it with a height reduced by the desired ratio. Think about it. Maybe it is due to the reduction in the basal area, or maybe it is due to the reduction in volume.

Your other claims about the sqrt roots are dependent on the units of measure that are used. I could claim that my height is the square root of 1,234,567,890 - if you use the right units.

[aquatus1]

I'm my own competition.

That's what happens when you come up with an answer that doesn't have a question.

[kmt_sesh]

You have not shown that the ratio is the square root of 5. What you have shown is that the ratio is approximately the square root of 5. You seem to think that square roots are special. Is there anything important in them? The answer to that depends on the context. In this case I see nothing special since you can't show a reason for it. In this context then, the square root of anything is of no interest.

When you laid out the construction you purposely tried to introduce the square root of 5 and did it in a rather bizarre way. You did it with no purpose other than to introduce the square root of 5. Consider the Egyptians. They don't know the Pythagorean theorem. They don't know about irrational numbers. They don't know about decimal expressions. Yet, you think that people completely unaware of any of this are going to consider the square root of 5 of interest.

What you need to do is to create a geometrical construction that introduces the square root of 5. That is what I originally meant. Figure out a construction which reduces the size of the the pyramid and leaves it with a height reduced by the desired ratio. Think about it. Maybe it is due to the reduction in the basal area, or maybe it is due to the reduction in volume.

Your other claims about the sqrt roots are dependent on the units of measure that are used. I could claim that my height is the square root of 1,234,567,890 - if you use the right units.

This raises an important point that I failed to mention in my previous post. For all of the posters who write about fancy mathematical expressions for the pyramids, how many are familiar with the math known and used by the Egyptians themselves? Parsing such monuments into modern mathematical formulae doesn't mean much if the exercise strays beyond mathematics we know the Egyptians used.

While there is scant evidence for mathematical applications in the Old Kingdom, mathematical papyri are known from later periods and reveal to us a number of approaches the Egyptians used in their engineering projects (such as seqed for determining slope). What Bennu needs to do is find tangible evidence that the square root of five was significant in ancient Egyptian culture (including engineering and building practices). While certain numbers were sacred or significant in ancient Egypt (e.g., eight and nine), I'm not sure how or if five played a significant part.

There's a lot of New Age fuss over "sacred geometry" and related concepts (especially where Giza is concerned), but much if not most of this is fantasy. As many of us have said many times at UM, if you look hard enough for something you want to see, you will see it eventually. I remember a poster in one forum or another who was convinced Giza was laid out to represent the Christian cross, and he posted a diagram showing where on the ground you could see it. Sure enough it was there. You just had to look hard enough—despite the fact that the earliest origins for Christianity lay over 2,500 years after Giza became a burial ground.

I'm not saying Bennu's idea is that far afield from the realm of logic because it certainly is not. All I'm cautioning is proving how the idea fits in with the culture and practices of Dynasty 4 Egypt. Context is everything.

[questionmark]

What I see as risible is that you take the AE out of its cultural context, place a frame over it that neither existed at the time and with some poetic license add a few things they did not know and bingo: We have a theory.

Anybody who takes a topographic map of Giza (and knows what he is seeing) will conclude within a few minutes that the pyramids were build in the fashion they were because there was no other space if they did not want to remove some hills and fill some valleys... which probably would have taken another 20-30 years.

Now, on a picture, given the size of the objects, those hills and valleys are not very noticeable.

[Bennu]

I think the Egyptians were interested in square root yielding geometric procedures for the purpose of surveying land. The procedure which yields the square root of 5, a 1:2 triangle or rectangle would have been important because 5 is an odd number and would be very difficult to calculate the side length of a land area which involves it. Suppose they wanted to mark a square area of 500 square units. How would they do it without that geometric method? Knowing the 1:2 triangle method, they could simply mark out a 100 x 200 unit right triangle and they would have the correct side length for the 500 square unit area.

It's actually known that they used such procedures. The "double remen", for instance, is the diagonal of a square of 1 cubit side length and the term remen is also used in regard to areas, as discussed here.

I can't say for certain that G3 height was derived from G1 height by such a geometric procedure. It's simply my own personal theory. I don't have to prove it. I'm not publishing it in a book or journal article. I merely present it as a topic for forum discussion, because I find it an interesting "coincidence".

That they used sqrt 2, sqrt 3 etc is amply demonstrated by the dimensions of the Giza rectangle, as I mentioned before. Who could possibly believe that a rectangle surrounding the three pyramids would be so close to sqrt 2 and sqrt 3 x 1000 by simply chance? The diagonal then of course yields sqrt 5. So that shows another method for obtaining sqrt 5. In this case, the diagonal from the NE corner of G1 to the SW corner of G3 is exactly sqrt 5 to two decimal places, it produces 5.008235103 when squared. So we have the square root of 5 in a very obvious Giza dimension, involving G1 and G3. It therefore makes perfect sense that G3 height should be G1 height divided by sqrt 5.

Edited August 14, 2014 by Bennu

[stereologist]

I think the Egyptians were interested in square root yielding geometric procedures for the purpose of surveying land. The procedure which yields the square root of 5, a 1:2 triangle or rectangle would have been important because 5 is an odd number and would be very difficult to calculate the side length of a land area which involves it. Suppose they wanted to mark a square area of 500 square units. How would they do it without that geometric method? Knowing the 1:2 triangle method, they could simply mark out a 100 x 200 unit right triangle and they would have the correct side length for the 500 square unit area.

It's actually known that they used such procedures. The "double remen", for instance, is the diagonal of a square of 1 cubit side length and the term remen is also used in regard to areas, as discussed here.

I can't say for certain that G3 height was derived from G1 height by such a geometric procedure. It's simply my own personal theory. I don't have to prove it. I'm not publishing it in a book or journal article. I merely present it as a topic for forum discussion, because I find it an interesting "coincidence".

That they used sqrt 2, sqrt 3 etc is amply demonstrated by the dimensions of the Giza rectangle, as I mentioned before. Who could possibly believe that a rectangle surrounding the three pyramids would be so close to sqrt 2 and sqrt 3 x 1000 by simply chance? The diagonal then of course yields sqrt 5. So that shows another method for obtaining sqrt 5. In this case, the diagonal from the NE corner of G1 to the SW corner of G3 is exactly sqrt 5 to two decimal places, it produces 5.008235103 when squared. So we have the square root of 5 in a very obvious Giza dimension, involving G1 and G3. It therefore makes perfect sense that G3 height should be G1 height divided by sqrt 5.

I simply do not believe you have any evidence to support these claims.

Do you have any evidence that the AE were interested in square roots?

Can you show that the AE were using surveying to lay out plots of particular sizes?

The link you posted refers to a remen area as a 50 by 100 unit area. The double-remen is not an expression of knowledge of a square root. Rather it is an approximation.

Again you are imposing mathematics derived much later onto the AE.

And you still cling to the idea that the relationship involves square roots and not some other number. The diagram in the OP is a forced relationship which is evident from your reverse engineering and display of 10 significant digits.

You have not shown that square roots are used in the dimensions of the Giza complex. You simply made that claim and now pretend it is true. Please show me what rectangle you placed over the Giza complex. Curious which of the infinite possibilities you chose. Then again you might want to check out a rectangle that is more likely to be the one at Giza. It is a 8 by 11 rectangle. It has a diagonal very close to the square root of 5, when the appropriate units are chosen.

[toast]

I think as long as the word "Wiltshire" in combination with the word "churches" will not appear, we can stay at

DEFCON 4.

Edited August 14, 2014 by toast

[Bennu]

Here's the Giza rectangle and sqrt 5 line. It's not 8 by 11. The height is 1732.374586 cubits and width is 1417.3161197. The height is therefore 1.222292 times the width. 11 divided by 8 is 1.375. They are, however, in an 11:9 ratio. I guess that explains why the width is not exactly sqrt 2 x 1000 but slightly over. Still, the height is obviously sqrt 3 x 1000. They just decided to make the width 9/11ths of that instead of the actual sqrt 2, for whatever reason. Maybe they wanted to show how close sqrt 3 and sqrt 2 are to 11:9. And, yes, the red line is slightly over sqrt 5 for that reason.

The straight N/S distance between the N side of G1 and S side of G2 also appears to be 7/11ths of the full height of the rectangle, height meaning the long side.The distance E/W appears to be 3/4 the full width of the rectangle. So I guess that messes up a lot of the overly complex theories about the pyramid positions. They do seem to be in simple ratios. It all starts from the rectangle long side being sqrt 3 x 1000 though. Of course, since 9 is not evenly divisible by 4 you can't use a single grid to match up with both the N/S and E/W positions of all three pyramids. All of this would support a unified Giza ground plan, rather than arbitrary placement as each was built.

Edited August 14, 2014 by Bennu

[kmt_sesh]

I think as long as the word "Wiltshire" in combination with the word "churches" will not appear, we can stay at

DEFCON 4.

Oh, dear, Very bad memory, that.

[Gingitsune]

The sum of 2, 3 and 5 is 9.

Isn't it... 10?, I mean 2 + 3 = 5, 5 + 5 = 10... no?

[questionmark]

Isn't it... 10?, I mean 2 + 3 = 5, 5 + 5 = 10... no?

Quite, but there are also mathematical equations demonstrating that humans eat with their ears...2 inches more or less...

[Bennu]

To explain the positions of the sides of all three Giza pyramids with a single grid of squares you would need to use a 36 x 44 grid of 39.3648 cubits, an odd number.

Edited August 14, 2014 by Bennu

[cormac mac airt]

Here's the Giza rectangle and sqrt 5 line. It's not 8 by 11. The height is 1732.374586 cubits and width is 1417.3161197. The height is therefore 1.222292 times the width. 11 divided by 8 is 1.375. They are, however, in an 11:9 ratio. I guess that explains why the width is not exactly sqrt 2 x 1000 but slightly over. Still, the height is obviously sqrt 3 x 1000. They just decided to make the width 9/11ths of that instead of the actual sqrt 2, for whatever reason. Maybe they wanted to show how close sqrt 3 and sqrt 2 are to 11:9. And, yes, the red line is slightly over sqrt 5 for that reason.

The straight N/S distance between the N side of G1 and S side of G2 also appears to be 7/11ths of the full height of the rectangle, height meaning the long side.The distance E/W appears to be 3/4 the full width of the rectangle. So I guess that messes up a lot of the overly complex theories about the pyramid positions. They do seem to be in simple ratios. It all starts from the rectangle long side being sqrt 3 x 1000 though. Of course, since 9 is not evenly divisible by 4 you can't use a single grid to match up with both the N/S and E/W positions of all three pyramids. All of this would support a unified Giza ground plan, rather than arbitrary placement as each was built.

It's not a unified ground plan if two of the 5 kings between Khufu and Menkaure didn't even have their tombs built on the Giza Plateau.

cormac

[Golden Duck]

Isn't it... 10?, I mean 2 + 3 = 5, 5 + 5 = 10... no?

Yep...it sure is. I cant even claim a 'typo' on that.

Just a plain an simple brain fart.