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# Giza Pyramid Height Relationships

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This image illustrates my theory about how the heights of khafre's and Menkaure's pyramids were derived from the Great Pyramid's height geometrically. It involves using the Great Pyramid's height of 280 cubits as the diagonal of a rectangle whose sides are in ratios of small whole numbers. The lengths of the "units" mentioned in the image are different for the two rectangles. The lengths of the units are not important, just that the rectangles are a 5:1 and a 2:1, both having the Great Pyramid's height as its diagonal. This is just my own theory, of course, but it seems to work out nicely. Could be the true basis for the heights.

Edited by Bennu

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“You b****** was thinking: there seems to be some growing dimensional instability here, swinging from zero to nearly forty-five degrees by the look of it. How interesting. I wonder what’s causing it? Let V equal 3. Let Tau equal Chi/4. cudcudcud Let Kappa/y be an Evil-Smelling-Bugger* (* Renowned as the greatest camel mathematician of all time, who invented a math of eight-dimensional space while lying down with his nostrils closed in a violent sandstorm.) differential tensor domain with four imaginary spin co-efficients. . .”

T. Pratchett, pyramids.

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This image illustrates my theory about how the heights of khafre's and Menkaure's pyramids were derived from the Great Pyramid's height geometrically. It involves using the Great Pyramid's height of 280 cubits as the diagonal of a rectangle whose sides are in ratios of small whole numbers. The lengths of the "units" mentioned in the image are different for the two rectangles. The lengths of the units are not important, just that the rectangles are a 5:1 and a 2:1, both having the Great Pyramid's height as its diagonal. This is just my own theory, of course, but it seems to work out nicely. Could be the true basis for the heights.

Would there be a purpose for the ancient Egyptians needing this as a basis for the heights?

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Would there be a purpose for the ancient Egyptians needing this as a basis for the heights?

...you mean besides the opportunity for Bennu to be one person in history to truly unlock the Secrets of the Pyramids?

--Jaylemurph

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...you mean besides the opportunity for Bennu to be one person in history to truly unlock the Secrets of the Pyramids™?

--Jaylemurph

Nope, that's the only reason, for me to be the only person on earth to unlock the secrets. Of course, if anyone else has an explanation for the seemingly arbitrary heights of the second two pyramids then perhaps THEY can be the only person on earth to unlock the secrets. Until then, looks like I have the only explanation, therefore the best one available. You might say that the second pyramid's height is simply the result of the base dimensions with a 3,4,5 triangle slope angle applied. That's possible, but then what about the third pyramid? It doesn't even have a pi based slope angle like the Great Pyramid. Close, yes, but not the same. What a coincidence, then, that dividing the height of the Great Pyramid by sqrt 5 yields its exact height. This perfectly explains why it's so small in comparison. Sqrt 5 is of course derived from a 1:2 rectangle, just like the one which forms the floor and ceiling of the King's Chamber. The heights being in the exact ratio of sqrt 5 seems a little unlikely to be mere coincidence to me.

Edited by Bennu

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Would there be a purpose for the ancient Egyptians needing this as a basis for the heights?

Needing it? No. Wanting it? Perhaps. It could be simple coincidence, but in the case of the third pyramid that seems unlikely. Not really any other obvious reason to make it so much smaller than the Great Pyramid. We know that the 1:2 rectangle was important, since the King's Chamber was based on it. It probably has to do with harmonic proportions or some kind of sacred proportions. The 5:1 rectangle does not appear to be contained anywhere in the Great Pyramid, though it is part of the ratio 3:4:5, on which the second pyramid's slope appears to be based. It would be appropriate then that this would be the pyramid with the 5:1 rectangle.

Edited by Bennu

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“You b****** was thinking: there seems to be some growing dimensional instability here, swinging from zero to nearly forty-five degrees by the look of it. How interesting. I wonder what’s causing it? Let V equal 3. Let Tau equal Chi/4. cudcudcud Let Kappa/y be an Evil-Smelling-Bugger* (* Renowned as the greatest camel mathematician of all time, who invented a math of eight-dimensional space while lying down with his nostrils closed in a violent sandstorm.) differential tensor domain with four imaginary spin co-efficients. . .”

T. Pratchett, pyramids.

What are you on? Because I want some.

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...you mean besides the opportunity for Bennu to be one person in history to truly unlock the Secrets of the Pyramids™?

--Jaylemurph

Lemme do that for you.

The Egyptians wanted to defeat death so they stacked a bunch of stones on top of each other over a very long period of time.

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Not really any other obvious reason to make it so much smaller than the Great Pyramid. We know that the 1:2 rectangle was important, since the King's Chamber was based on it. It probably has to do with harmonic proportions or some kind of sacred proportions.

The economic situation wasn't an obvious reason?

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Nope, that's the only reason, for me to be the only person on earth to unlock the secrets. Of course, if anyone else has an explanation for the seemingly arbitrary heights of the second two pyramids then perhaps THEY can be the only person on earth to unlock the secrets. Until then, looks like I have the only explanation, therefore the best one available.

I see that, much like all the truly great pseudo-historians of the world, you are by no means crippled by modesty.

--Jaylemurph

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The problem with ratios is well known in mathematics and sciences. An example is Simpson's problem. Another was the long standing mistake that people lose cells in their hippocampus as they age.

Here we have a related problem and that is attempting to match up numbers. In this case a ratio of geometric values is being matched up to other geometric ratios that are not related. It is even noted in this thread that some of the geometric ratios do not match, i.e. a ratio is not always pi.

Let's go back to the drawing in the OP. There are numbers there that are improperly written numbers. There are too many decimal places for the heights of the G2 and G3. If the measurement of the G1 is only 3 digits of precision, then the G2 and G3 are probably the same. They should be 275 and 125 respectively. The 10 digits of precision in the drawing do not exist. These values appear to be computed rather than measured. So let's see what happens when I use the realistic values of 275 and 125.

The first ratio comes out to be 5.22, not 5.

The second ratio comes out to be 0.51.

It would appear that the simple geometric ratios are not stable. The simple ratios are not stable, especially the ratios when the heights are similar in value.

I would simply have to consider this claim as incorrect simply based on mathematical considerations.

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I see that, much like all the truly great pseudo-historians of the world, you are by no means crippled by modesty.

--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".

Regarding the smaller size of the third pyramid being due to cost restrictions, I would have to wonder why the king would have used granite instead of limestone for the first 16 courses if he was tight on cash. He also used granite for part of one of the three satellite pyramids. He had fancy statues made etc. I really don't think he was that poor. It's possible that he did need to make a smaller one, or that he wanted to be more modest than his predecessors and use funds for more practical purposes, but we still must wonder why that exact size. It could have been any randomly smaller size. What are the odds of the height coming out to exactly the Great Pyramid's height divided by sqrt 5?

Also, the side lengths of the second two pyramids are odd and seemingly inexplicable unless you believe the theories of John Legon. It is possible that he's right about the side lengths but he has no explanation for the heights. You would expect Menkaure's pyramid to have been either a pi pyramid or a 3,4,5 pyramid, yet it is neither exactly. The slope is a little too low for a pi pyramid.

Anyway, I just made these observations about the geometric relationship between the three pyramid heights. It seems like an interesting observation to me. It's just one more way to show the amazing geometric relationships of the pyramids. John Legon's was another way. Since his observations don't involve the heights, we can both be right. My observations simply add to those already made by him regarding the base sizes and positions of the pyramids.

Edited by Bennu
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The problem with ratios is well known in mathematics and sciences. An example is Simpson's problem. Another was the long standing mistake that people lose cells in their hippocampus as they age.

Here we have a related problem and that is attempting to match up numbers. In this case a ratio of geometric values is being matched up to other geometric ratios that are not related. It is even noted in this thread that some of the geometric ratios do not match, i.e. a ratio is not always pi.

Let's go back to the drawing in the OP. There are numbers there that are improperly written numbers. There are too many decimal places for the heights of the G2 and G3. If the measurement of the G1 is only 3 digits of precision, then the G2 and G3 are probably the same. They should be 275 and 125 respectively. The 10 digits of precision in the drawing do not exist. These values appear to be computed rather than measured. So let's see what happens when I use the realistic values of 275 and 125.

The first ratio comes out to be 5.22, not 5.

The second ratio comes out to be 0.51.

It would appear that the simple geometric ratios are not stable. The simple ratios are not stable, especially the ratios when the heights are similar in value.

I would simply have to consider this claim as incorrect simply based on mathematical considerations.

The problem with your statements is that I was simply giving the precise heights that result from the geometric procedure I showed. I was not suggesting that the actual finished heights were those figures. I simply maintain that the geometric ratios shown were the intended heights, not the actual heights. They would have rounded them off to whatever was the closest dimension obtainable using Royal Cubits and their standard subdivisions as the seked of the pyramid's slope. Tell me this, do you seriously think that Menkaure's Pyramid height being pretty much exactly, like within a few inches, the Great Pyramid's height divided by sqrt 5 happened by simple chance? That seems like an awfully unlikely chance occurrence to me. Then when the same procedure using another small whole number ratio, 5:1, can be used to produce Khafre's Pyramid height, it seems even less unlikely to be simple chance. It's possible, yes. It's possible that the Great Pyramid is so similar to a squared circle by simple chance too, but how likely is it?

Edited by Bennu

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I'm not saying that this is some great discovery. Merely that it's an obvious thing which nobody seems to have noticed before, paricularly in the case of Menkaure's Pyramid. Somebody really should have noticed the obvious sqrt 5 ratio, being that the 1:2 rectangle is part of the King's Chamber dimensions. How it was missed I really don't know. I guess nobody ever bothered to divide the pyramid heights by each other before. Strange really. That's how I discovered this. I simply divided the Great Pyramid's height by the third pyramid's height and couldn't help but notice that it was sqrt 5.

Edited by Bennu

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If we take the three great Gaza Pyramids isolated we could come to the conclusion that some funny math was involved. The problem to this is that there were older attempts with other measurement relations that were flops. What the architects did was to keep on doing what worked.

As for math, the math books we found from the pyramiditis time tell us that if you need a square root or in fact anything more complicated than the area of a triangle you are out of luck, they were unknown to them. See Moscow Papyrus ~1800 BC and Ahmes Papyrus (1650, copied from a document from ~ 2000 BC).

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If we take the three great Gaza Pyramids isolated we could come to the conclusion that some funny math was involved. The problem to this is that there were older attempts with other measurement relations that were flops. What the architects did was to keep on doing what worked.

As for math, the math books we found from the pyramiditis time tell us that if you need a square root or in fact anything more complicated than the area of a triangle you are out of luck, they were unknown to them. See Moscow Papyrus ~1800 BC and Ahmes Papyrus (1650, copied from a document from ~ 2000 BC).

They may not have known how to calculate square roots but it seems likely that they knew that the diagonal of a 1:2 rectangle was the side length of a square with an area of 5 square units. The Pythagorean Theorem came from Egypt after all.

Edited by Bennu
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This image illustrates my theory about how the heights of khafre's and Menkaure's pyramids were derived from the Great Pyramid's height geometrically. It involves using the Great Pyramid's height of 280 cubits as the diagonal of a rectangle whose sides are in ratios of small whole numbers. The lengths of the "units" mentioned in the image are different for the two rectangles. The lengths of the units are not important, just that the rectangles are a 5:1 and a 2:1, both having the Great Pyramid's height as its diagonal. This is just my own theory, of course, but it seems to work out nicely. Could be the true basis for the heights.

Could be. Or perhaps this could be the answer.

SC

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The problem with your statements is that I was simply giving the precise heights that result from the geometric procedure I showed. I was not suggesting that the actual finished heights were those figures. I simply maintain that the geometric ratios shown were the intended heights, not the actual heights. They would have rounded them off to whatever was the closest dimension obtainable using Royal Cubits and their standard subdivisions as the seked of the pyramid's slope. Tell me this, do you seriously think that Menkaure's Pyramid height being pretty much exactly, like within a few inches, the Great Pyramid's height divided by sqrt 5 happened by simple chance? That seems like an awfully unlikely chance occurrence to me. Then when the same procedure using another small whole number ratio, 5:1, can be used to produce Khafre's Pyramid height, it seems even less unlikely to be simple chance. It's possible, yes. It's possible that the Great Pyramid is so similar to a squared circle by simple chance too, but how likely is it?

The problem is that you manufactured numbers to obtain the results you desired. My calculations show that your claim of a sqrt(5) may not be correct. The 5:1 does not appear to exist. It is a number you picked from a range of possibilities. In fact, you manufactured that ratio by forcing the numbers to be what you needed. The GP is similar to a "squared circle" due to an artifact of the construction process.

I certainly see no reason to support this idea.

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They may not have known how to calculate square roots but it seems likely that they knew that the diagonal of a 1:2 rectangle was the side length of a square with an area of 5 square units. The Pythagorean Theorem came from Egypt after all.

The Pythagorean theorem was not know at the time you suggest. If you look at that theorem you will see that the theorem was proved using areas and not lengths.

If you want to show that the sqrt(5) is introduced into the construction, then you need to show how someone would lay out a pyramid of one size and construct another that involves a sqrt(5). This is a geometry problem and you need to do that without claiming people had knowledge of the value of the sqrt(5).

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The Pythagorean theorem was not know at the time you suggest. If you look at that theorem you will see that the theorem was proved using areas and not lengths.

If you want to show that the sqrt(5) is introduced into the construction, then you need to show how someone would lay out a pyramid of one size and construct another that involves a sqrt(5). This is a geometry problem and you need to do that without claiming people had knowledge of the value of the sqrt(5).

Unfortunately, there's no way to know how they actually did it. Any number of ways could be proposed. They would have known the height of the GP so it was just a matter of constructing a 1:2 rectangle with that diagonal. Maybe just by drawing a 1:2 triangle or rectangle in the sand in a flat area with the short side being a dimension close to what would be required, like 100 cubits. Then after that was drawn, extending the diagonal with a rope until it reaches 280 cubits. Then extending the short side until a 90 degree rope from it would hit the end of the 280 cubit diagonal. They could have done it on a smaller scale first, like 28 cubits, then scaled the results up later. I could envision a few different ways.

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Unfortunately, there's no way to know how they actually did it. Any number of ways could be proposed. They would have known the height of the GP so it was just a matter of constructing a 1:2 rectangle with that diagonal. Maybe just by drawing a 1:2 triangle or rectangle in the sand in a flat area with the short side being a dimension close to what would be required, like 100 cubits. Then after that was drawn, extending the diagonal with a rope until it reaches 280 cubits. Then extending the short side until a 90 degree rope from it would hit the end of the 280 cubit diagonal. They could have done it on a smaller scale first, like 28 cubits, then scaled the results up later. I could envision a few different ways.

That is not going to work. A rope 280 cubits in length would have too much stretch. There would be a large uncertainty in that method.

You claim you are going to draw a triangle that has the proper ratios. Why do you do that? What is the purpose in doing this? Do you think that the start of a pyramid project is to determine the desired height?

What about the other pyramid? Slight changes in that pyramid's height have large changes in the ratio. I rounded your number which was a 0.2% change in the number and ended up with a ratio that went from 1:5 to 1:5.22. That changed the ratio from a simple one to a nonsimple ratio.

The AE did simple arithmetic. My guess is that if they tried to halve the height they missed by a little bit.

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Could be. Or perhaps this could be the answer.

SC

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".

Edited by Bennu

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I could envision a few different ways.

Which leads us to math infinite... or non existent.

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Which leads us to math infinite... or non existent.

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?

Edited by Bennu

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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.

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?

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