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# Great Pyramid Coffer Dimensions Solved

## 32 posts in this topic

This is my theory of how the outer dimensions of the Great Pyramid's coffer were arrived at. It is all about certain square roots.

Firstly, I should state that the remen used in this theory is the Royal Cubit divided by sqrt 2, or 14.58 inches (rounded to two places), and the Royal Cubit length used is 20.62 inches, as established by Flinders Petrie. The dimensions used for the coffer were obtained from this page. They are within a small fraction of an inch of what I calculated myself from Petrie's measurements.

OUTER DIMENSIONS:

Height = 1048 mm = 41.26 in. = 3.4 ft

Width = 977 mm = 38.46 in. = 3.2 ft

Length = 2278 mm = 89.68 in. = 7.47 ft

The height appears to be simply 2 Royal Cubits, which at 20.62 inches would be 41.24 inches. This could also be viewed as one remen x sqrt 8

The width is one remen x sqrt 7, which would be 38.575 inches. Using Royal Cubits it would be x sqrt 3.5. Since that's not a whole number I have to assume that the remen was used for this dimension.

The length is one remen x sqrt 38 or one Royal Cubit x sqrt 19. Since 19 is a more practical number to deal with, I'm assuming that the cubit was used for this dimension. This would be 89.88 inches.

Why would the builders have an interest in the number 19? Hard to say but here are some possibilities;

The power of the number 19 and its proper use was a fundamental teaching in the Ancient Egyptian Temple Science. One of the primary grids used in Ancient Egypt to lay out designs on the Temple walls was the grid based on 19 vertical divisions; this is known to Egyptologists, but they have no idea of the significance of this fact. In brief, the number 19 is built into the spiritual blueprint of the human being and all of creation. It is related to an energetic grid surrounding every human being, which contains within it the precise positions and functions for all of the spiritual energy centers in the human being (not only chakras, but a large number of power centers not taught publicly by any tradition even today.)

The Egyptian priesthood knew that the Grid of 19 was in reality the background of the human archetypal energy blueprint. They also knew that the correct use of the 19 in design (as 19 design elements, or by building the number into measurement and proportional systems in design) creates a very powerful emanation of beneficial energy; this is the Golden Light often referenced in ancient Egyptian texts as essential for spiritual development and for consciousness after death.

http://www.spiritofmaat.com/mar08/sacred_geometry.html

So I suspect that it was intended to confer some sort of beneficial effects on the coffer.

Edited by Bennu

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I don't think they had an interest in any particular number. I do, however, think it was the right size to accommodate the wooden sarcophagus -- and that this object was to a specific dimension because of the size of the king and number of interior coffins.

Had it been to some specific number, we would see this repeated in other sarcophagi AND there would have been some references in the texts about these numbers.

http://news.yahoo.com/fit-king-largest-egyptian-sarcophagus-identified-174734638.html

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I don't think they had an interest in any particular number. I do, however, think it was the right size to accommodate the wooden sarcophagus -- and that this object was to a specific dimension because of the size of the king and number of interior coffins.

Had it been to some specific number, we would see this repeated in other sarcophagi AND there would have been some references in the texts about these numbers.

http://news.yahoo.co...-174734638.html

Not necessarily. Maybe the GP was a special case. Do the other pyramids have a Grand Gallery and two chambers up above ground level? There is nothing typical about the GP. Do you seriously expect me to believe that all three coffer dimensions can be obtained to within a fraction of an inch through multiplying remens or cubits by square roots through simple chance? Is the coffer's height 2 cubits by simple chance? Then why should the other two dimensions be? The only other explanation put forward, like yours for instance, is just arbitrary sizing to the general shape of a human body and coffin. I don't find that at all convincing, sorry. I haven't checked the dimensions of Khafre's and Menkaure's coffers. Maybe they also have mathematical/geometrical relationships.

Edited by Bennu

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I just checked the Khafre coffer dimensions and they are length 5 cubits, height one remen x sqrt 7 and width 2 cubits. So the height and width are the same as the GP coffer but switched around. The length is simpler than the GP coffer, an even 5 cubits. But then why is the GP coffer length not 5 cubits also? The khafre coffer dimensions can be found here. Petrie doesn't provide the dimensions of Menkaure's coffer and it is lost. I guess that's the one that sunk with the ship that was carrying it to Britain.

Edited by Bennu

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Not necessarily. Maybe the GP was a special case. Do the other pyramids have a Grand Gallery and two chambers up above ground level? There is nothing typical about the GP. Do you seriously expect me to believe that all three coffer dimensions can be obtained to within a fraction of an inch through multiplying remens or cubits by square roots through simple chance? Is the coffer's height 2 cubits by simple chance?

When you get to mess around with various square roots, why, yes, that's exactly what it is.

Perhaps you can show us where the evidence is for the Egyptian knowledge of the square root of 2 or 3 or 5 or 7 or 8?

Harte

Edited by Harte

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When you get to mess around with various square roots, why, yes, that's exactly what it is.

Perhaps you can show us where the evidence is for the Egyptian knowledge of the square root of 2 or 3 or 5 or 7 or 8?

Harte

The coffer and the Giza rectangle.

Edited by Bennu

So, no, then?

--Jaylemurph

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Not necessarily. Maybe the GP was a special case.

This was for a god, who was the son of a god and the father of the gods. If it was significant, then it would be repeated for the other god-kings and later for the nobles. A good example of this is the Pyramid texts or the use of the opener-of-mouths and so forth. If it's supposed to be special and significant, then you need to explain (culturally) the lack of consistency.

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The coffer and the Giza rectangle.

That doesn't show that they knew square roots, but it may show a preferred proportion. We know that they did these calculations 2,000 years later but they did not associate them with anything religious as far as we can tell.

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They could do this. The left edge is 1 unit, either a remen or a cubit, whichever is required. The top and bottom lines are sqrt 7 at the first red line and sqrt 19 at the second red line. Does this look like it requires a knowledge of advanced mathematics? If anyone doubts my theory then please explain why the coffer is sqrt 19 cubits long instead of a nice even 5 cubits like Khafre's.

Edited by Bennu

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They could do this. The left edge is 1 unit, either a remen or a cubit, whichever is required. The top and bottom lines are sqrt 7 at the first red line and sqrt 19 at the second red line. Does this look like it requires a knowledge of advanced mathematics? If anyone doubts my theory then please explain why the coffer is sqrt 19 cubits long instead of a nice even 5 cubits like Khafre's.

Khafre was taller.

Seriously, you're gonna have to compare to more than one other sarcophagus. You have to show these square roots all over, not just one sarcophagus.

Unless you want to claim that Khufu was the Square Root King.

While you're at it, calculate 22/7, then compare that number to the "pi calculation" that the fringe love so much and note the error. Then compare the woo calculation of the pyramid "pi" to pi itself and note that error.

Which error is greater? What is the percent difference from pi for each number?

Harte

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There is no significant error in the GP pi pyramid. As I stated before, a perfect pi pyramid with a height of 280 cubits would have sides of 439.82 cubits. You wrote the following on my pyramid heights thread;

From Petrie;

North Side...... 9069.4 inches...... 439.84 Royal Cubits

East Side........ 9067.7 inches ..... 439.75 Royal Cubits

South Side ......9069.5 inches ......439.84 Royal Cubits

West Side .......9068.6 inches ......439.81 Royal Cubits (all four rounded to nearest hundredth)

That looks like they got it right, to within 2/100s of an inch, on two sides and 1/100th of an inch on one. The side with the largest error was off by a whopping 7/100ths of an inch. Shame on them. If they had used 22/7 the sides would have been 440 cubits, which apparently they are not.

Edited by Bennu

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There is no significant error in the GP pi pyramid.

They changed the slope, you know. Had to do with the stability of the materials.

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There is no significant error in the GP pi pyramid. As I stated before, a perfect pi pyramid with a height of 280 cubits would have sides of 439.82 cubits. You wrote the following on my pyramid heights thread;

From Petrie;

North Side...... 9069.4 inches...... 439.84 Royal Cubits

East Side........ 9067.7 inches ..... 439.75 Royal Cubits

South Side ......9069.5 inches ......439.84 Royal Cubits

West Side .......9068.6 inches ......439.81 Royal Cubits (all four rounded to nearest hundredth)

That looks like they got it right, to within 2/100s of an inch, on two sides and 1/100th of an inch on one. The side with the largest error was off by a whopping 7/100ths of an inch. Shame on them. If they had used 22/7 the sides would have been 440 cubits, which apparently they are not.

So, you decided not to compare the two "pi's?" Is that it?

Why do you claim it's a "pi pyramid" yet refuse to compare the calculations made by the fringe to the values of pi and 22/7?

The fringe calculation: 2 times a base length divided by the height. This is where the claim of pi actually comes from - a random series of arithmetical operations.

Base length: 230.38 meters

Height: 146.6 meters.

Carry enough decimals to compare:

pi = 3.1415926535897932384626433832795

2/7 = 3.1428571428571428571428571428571

The woo calculation: 3.1429740791268758526603001364256

Perhaps you'll notice exactly how close to 22/7 the woo calculation comes and that it differs far more greatly from pi than it does from 22/7

Remember, I already told you that the AE's constructed angles by a specific number of fingers "in" (horizontally) for every cubit "up" vertically. That they measured angles this way is an established fact. The GP was constructed at an angle of 22 fingers in for every one cubit (28 fingers) up.

Since the "in" applies only to half the side length (the pyramid vertex aligns with the center of the structure,) you should be able to see that the ratio of 2 bases to one height has four times the number of base lengths as the actual Egyptian calculation of 22/28. (Two base lengths [woo]compared to one-half base length [AE's].)

So (4x22)/28 = 22/7 and there you go.

No "pi pyramid" at all.

Makes perfect sense, since the AE's didn't know pi until the Greeks gave it to them.

You should have done this yourself. I pointed it out. Why do I have to calculate this for people every time it comes up?

Harte

Edited by Harte
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Be that as it may, the side lengths are still not 440, as they would be if it were a simple 22/7 pyramid. You can't explain that. And the seked thing is from much later than the 4th Dynasty. Only the priests of Giza knew the secrets of making a pi pyramid. And Khafre was not taller. He was exactly the same size as his pappy so why did his pappy have a coffer that was sqrt 19 cubits?

Edited by Bennu

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The coffer and the Giza rectangle.

That's wrong. That's your interest in square roots. You need to show that the AE had knowledge of these values.

You are simply looking for square roots instead of examining the evidence. That is the sort of thing numerologists do: they perform mathematical operations for no purpose other than to look for hits and disregard all of the misses.

These height, width, length claims are rather contrived.

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The sides are not 440 according to modern measurements and a conversion of 20.62"/cubit. If the conversion is changed every so slightly then the sides are 440. This suggests that 2 obvious possibilities.

1. The conversion is not correct, it could be 20.61"/cubit

2. The AE were not able to measure to 4 digits of precision in their time

You seem to be quite lost with the math. The approximation for pi at 22/7 is closer than the true value of pi. You can't explain that.

You don't need any secrets to build a so-called pi pyramid. Your claim that "Only the priests of Giza knew the secrets of making a pi pyramid" is a rather fanciful fairy tale. Another simple way to introduce pi is to use a stick to measure vertically and use that stick as a diameter for a wheel to measure distance. Count turns of the wheels to measure distance. Count sticks to measure height. That introduces pi. The builders only have to count. No tricky math required, only counting.

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I suppose it's possible that the cubit was not exactly 20.62", but it looks like it would be a little longer than that, rather than shorter, if any adjustment is in fact required. This is based om the King's Chamber measurements, assuming that it was intended to be 10 x 20 cubits.

Regarding the use of pi, it wasn't necessary for them to know the mathematical value but simply to know how to get the radius to perimeter ratio correct through simple geometric procedures. That's why I showed the diagram in my recent posts. To show how they got sqrt 7 and 19 through very simple geometry. As the image shows, they could get the sqrt of any whole number simply by drawing arcs.

Edited by Bennu
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While it's true that square roots can be generated by simple construction with compass (rope and stake) and strait edge, it's also true that the Egyptians had no mathematics of ratios.

The fractional parts they used were parts of a whole only and weren't expressed in any way that would be mathematically manipulable like we do today. Besides, pi cannot be expressed as a ratio. That's why they call them "irrationals."

The Egyptians were, however, aware of a mysterious number relationship between a circle's diameter and it's circumference. Without looking it up, my memory (faltering, admittedly) tells me they started out simply using the number 3 for it, and wen't on eventually (much later) to use the very same ratio I've given here several times - 22/7. But (obviously) that's not how they expressed it.

The concept of a square root, other than whole square roots, never entered their methods, IIRC. But they did know about diagonals of squares and rectangles so you could look at it that way.

Harte

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I suppose it's possible that the cubit was not exactly 20.62", but it looks like it would be a little longer than that, rather than shorter, if any adjustment is in fact required. This is based om the King's Chamber measurements, assuming that it was intended to be 10 x 20 cubits.

Regarding the use of pi, it wasn't necessary for them to know the mathematical value but simply to know how to get the radius to perimeter ratio correct through simple geometric procedures. That's why I showed the diagram in my recent posts. To show how they got sqrt 7 and 19 through very simple geometry. As the image shows, they could get the sqrt of any whole number simply by drawing arcs.

Although anyone could make a construction such as you show it does not suggest that it was understood that the value was a square root or that it was a square root such as you suggest.

Suppose you stumble onto the knowledge that a 3-4-5 triangle is a right triangle. Does that tell you that 3 squared plus 4 squared is 5 squared? No. It might just be a fortuitous discovery that this is a way to make a right angle. The understanding that there is an unlimited number of such right triangles with integer sides is not reported for thousands of years. The Pythagorean theorem about the areas being equal is not reported for thousands of years either.

So although you can show constructions of values which you are interested in I do not see evidence that the AE used such values or were interested in such values.

Consider this. You think that the AE are square-root-ites. Suppose that is true. Then correct all of your cubit conversions to determine the length of the cubit.

If the chamber is sqrt(19) cubits, then a cubit is 20.57".

If the chamber is sqrt(3.5) cubits, then the cubit is 20.55".

So if your square root idea is correct, then the length of the cubit is not as precise as you originally thought and it lowers the AE constructions from 4 digits of precision to 3.

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Suppose you stumble onto the knowledge that a 3-4-5 triangle is a right triangle. Does that tell you that 3 squared plus 4 squared is 5 squared? No. It might just be a fortuitous discovery that this is a way to make a right angle. The understanding that there is an unlimited number of such right triangles with integer sides is not reported for thousands of years. The Pythagorean theorem about the areas being equal is not reported for thousands of years either.

From the found papyri we know that they had an easier method to make a 90 degree angle:

you take a piece of rope and on a straight line you make two circles (I made them different sizes to show that it works in all cases) or semi circles. You draw a line through the outer points where the circles meet and bingo, a 90 degree angle.

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Yeah that does look like a handy way to make a 90 degree angle. Regarding the square roots, I guess they somehow figured out how to get the ratio of a rectangle's diagonal to its side lengths. It just seems like too much of a coincidence for the coffer's length and width to both be square root multiples, when there doesn't appear to be any other reasonable explanation for the seeming odd dimensions. You could suggest that it was just arbitrary, but I don't think anything about the GP is arbitrary. It all looks very well planned. If the coffer size was based on Khufu's body size, I still think the builders would have used the closest round numbers of units, just to make it easier to execute.

Edited by Bennu

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Yeah that does look like a handy way to make a 90 degree angle. Regarding the square roots, I guess they somehow figured out how to get the ratio of a rectangle's diagonal to its side lengths.

Not very hard at at all.

You lay out the rectangle/square, place a stick across the diagonal, mark and then cut.

Instant diagonal measurement standard - no knowledge of square roots required.

Harte

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Not very hard at at all.

You lay out the rectangle/square, place a stick across the diagonal, mark and then cut.

Instant diagonal measurement standard - no knowledge of square roots required.

Harte

My point exactly. Or to do it on a large scale, like the Giza necropolis, you use long ropes. To get sqrt 3 x 1000 cubits, you draw a regular triangle within a circle with a radius of 1000 cubits. Incidentally, it is rather obvious that a cummunal tomb for the Giza kings is located at the center of the hexagram, probably about 100 cubits down, possibly with a secret tunnel from the Sphinx or the pyramids.

Edited by Bennu

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Here's where the tomb is. This is a 1:2 right triangle with a long side of 200 cubits and short side of 100.

Edited by Bennu

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