Am I right in thinking that the brightest object in the sky after the sun and moon is Venus?
I suppose the ancient Egyptians regarded the stars and wandering stars (planets) as very much smaller than the sun and moon in the third millennium BC.
It seems natural for the kings of Egypt in the Pyramid Age to have identified themselves with the sun and the moon as the greater light governing th
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Mark Heaton
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Ancient Egypt
You have created a theory which has powerful argument against it.
It is essentially the same as Piazzi Smyth's theory for which there is no documentary evidence, merely a construction of numbers based on pyramid dimensions, which is in stark contrast to my theory of Khafre's pyramid which is based on its harmony with documentary evidence in ways which have been overlooked.
Piazzi
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Mark Heaton
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Ancient Egypt
The following observation is the kind I have in mind:
The volume of a pyramid can be calculated from the height and the slope of the faces.
For Khafre's pyramid the cotangent of the sloping faces is equal to 1/4 + 1/4 + 1/4
Volume of Khafre's pyramid is (1/4 + 1/4 + 1/4) x cube of height
In modern maths:
Cotangent = 3/4
Volume = 3/4 x h x h x h
Now if we think the
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Mark Heaton
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Ancient Egypt
Hi Brendan,
I have written an academic style paper since Easter which is currently 6700 words including a conclusion, but I need to edit / check before sharing with one or two people perhaps including Keith Hamilton.
The last three sentences may be as follows:
Further research may reveal other aspects of the internal architecture, but some aspects may require a more detailed survey. The
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Mark Heaton
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Ancient Egypt
Hi Brendan
The proposed design (my model) would be strange if the only reason for such a complex design was a roof area of 274 square cubits.
If this had been the only objective then it could have been done much simpler.
The geometric model in my mind explains the double square 19 x 9.5 and the double square 20 x 10 and two identical rectangles.
I think the first step is to arrive a g
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Mark Heaton
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Ancient Egypt
Yes
The sloping faces of Khafre's pyramid conform to a rise of 4 for a run of 3 so a slope length of 5 which is the triplet you mention.
I think this is an important feature of the design, but first let's look at a simple proposition:.
It is proposed that the peaked roof of the burial chamber was designed to to have an area of 274 square cubits as the architect’s signature on
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Mark Heaton
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Ancient Egypt
Thanks for that.
On Wiki it mentions a 10 metre difference in the level of the bases so say 20 cubits as you point out.
The apek of Khafre's pyramid would then be 14 cubits higher than Khufu's pyramid when it was built, as you also point out.
The floor of Khafre's chamber is 14 cubits higher than the base of the Great Pyramid if the the long walls have another geometric di
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Mark Heaton
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Ancient Egypt
Hi Kanga,
Thanks for your contribution.
I agree with Butler that the intended height of Khafre's pyramid was 274 cubits.
The original height of Khafre's pyramid (274 cubits) appeared to be higher than Khufu's Pyramid by about 4 cubits if the base was 10 cubits higher than Khufu's base because Khufu's pyramid was 280 cubits:
274 + 10 - 280 = 284 - 280 = 4
The
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Mark Heaton
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Ancient Egypt
Has anyone on this forum considered the geometry of Khafre's burial chamber?
I can't find anything relevant on the Hall of Maat search.
The geometry appears to be hugely significant.
Petrie spotted that the long walls have a double square of '20 x 10', dividing its length of 27 cubits into 20 cubits and 7 cubits.
The floor has a a double square '19 x 9.5'
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Mark Heaton
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Ancient Egypt
Thanks for that.
It appears that the ceilings of the stress relieving chambers were dressed better than the floors in the illustrations I have just looked at, and also from the notes of Maragioglio and Rinaldi.
I suppose that it would be more logical to consider ceiling levels rather than floor levels given that it is the ceiling of the crypt of the King's Chamber which is at a conspic
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Mark Heaton
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Ancient Egypt
The ceiling of the King’s Chamber of the Great Pyramid is made of 9 huge granite beams of granite with the level of the ceiling at a third of the height of the complete pyramid within a very small fraction of a cubit (280/3 cubits) from Petrie’s survey.
The formula for the volume of a pyramid is the area of the base multiplied by a third of the height (H/3), and the ratio of the area of base t
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Mark Heaton
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Ancient Egypt
The only relatively new paper that I have been able to track down was published in Mediterranean Archaeology and Archaeometry Vol 2, pages 111 to 125 and entitled 'The Mathematics of Pyramid Construction in Ancient Egypt'.
This paper contains quite a lot on MMP problem number 14 including a new proposition by its author, Flora Vafea, on how the ancient Egyptians may have worked out
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Mark Heaton
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Ancient Egypt
Thanks for the good advice, but libraries and museums are closed to the general public in England at this time, as is EES, but it would be possible for me to buy yet another publication on the internet.
Page 49 of the Rhind Mathematical Papyrus by Robins and Shute provides a mathematical proof of the formula for the volume of a truncated pyramid using algebra based on the subtraction of the vo
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Mark Heaton
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Ancient Egypt
Can you show me how Gillings derived the formula. Was it as follows?
Using your notation and assuming the formula for the volume of a pyramid:
Let VCP = Volume of complete pyramid = a x a x 1/3 x k = 4 x 4 x 1/ 3 x 12 = 64
Let VP = Volume of small virtual pyramid projected by pyramid = b x b x 1/3 x L = 2 x 2 x 1/3 x 6 = 8
Let VTP = Volume of Truncated Pyramid = VCP - VP = 64 - 8 = 56
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Mark Heaton
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Ancient Egypt
Hi Kanga,
Thanks for your post.
Yes, the formula for volume of a pyramid is apparent from the special case of the division of a cube into 6 pyramids with a slope of 45 degrees (seked of 7 palms).
Empirical evaluations may have revealed that the volume of all pyramids can be calculated from this formula.
The volume of a pyramid is mean cross-sectional area multiplied by height so it fo
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Mark Heaton
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Ancient Egypt
Yes,
Quote from her book
The most common fault in many theories, however, is the liberal use of modern mathematical concepts in the attempt to explain the design of ancient monuments. Yet scholars such as Ludwig Borchardt, Jean-Philippe Lauer and Gay Robins have proved that it is possible to explain the geometry of pyramids (and not only of the Great Pyramid) by using proper mathematical i
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Mark Heaton
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Ancient Egypt
I can't find anything in the literature explaining the formula for the volume of a truncated pyramid in relation to Horus-eye fractions.
There is a relationship which appears to have been overlooked which provides an insight into how the formula was understood, though not necessarily how the formula was discovered which I think could have been determined empirically.
The formula in the
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Mark Heaton
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Ancient Egypt
I tend to agree that we should consider the geometry first, which may then provide a reason why the geometry was chosen.
For example, the niche in the so-called Queen's Chamber was probably for the king's statue or ka statue, and is displaced from the centre of the chamber by eight and a half palms or 34 digits, precisely so based on Petrie's measurements near the base, so by 25
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Mark Heaton
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Ancient Egypt
Hi Robin,
My recollection of Smyth's survey around the plug block was that he thought he may not have accomplished it very accurately, so I compared to Petrie's determination.
From memory Petrie's determination was precisely the same as Smyth's determination accurate to a small fraction of an inch.
It should be remembered that Petrie wanted a rigorous set of measurem
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Mark Heaton
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Ancient Egypt
Hi Hermione,
Yes, I searched the archive in one of the two ways after my post, and before your post.
I didn't find anything.
Problem no 14 in the MMP should, perhaps, have informed debates on the seked.
My review and evaluation of problem no 14 is currently based on the papers of Thomas and Vetter (in JEA) as I haven't yet seen the papers by Gunn & Peet or Vogel which ar
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Mark Heaton
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Ancient Egypt
I started researching websites etc earlier this month having looked at problem no 14 on the volume of a truncated pyramid over 15 years ago.
T. E. Peet, Brunner Professor of Egyptology at the University of Liverpool, left posterity with an article on Mathematics in Ancient Egypt as an amplification of a lecture given in the Rylands Library on 11th February 1931.
This article includes the f
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Mark Heaton
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Ancient Egypt
For me this about the balance of evidence in its historical context so probability rather certainty.
The base of sarcophagus is at the level where the area of the triangular cross-sections of the pyramid is divided into 2 sections with the same area, and each half is equal to the area of a semi-circle with the circle's diameter equal to the height of the pyramid, as calculated from the pi
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Mark Heaton
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Ancient Egypt
Yes, I think many alternative ideas are tenable, although different ideas can be mutually exclusive.
I decided to post on the spur of the moment after reading through some of my notes from a few years ago which I had forgotten, so almost like reading a theory from someone else, but later wondered if I had already raised this topic on this forum.
Petrie labelled the theories of the sarcophag
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Mark Heaton
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Ancient Egypt
I try to avoid websites I don't know as my 2005 computer has little or no security, but if you can make the point yourself then I will try to answer.
Mark
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Mark Heaton
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Ancient Egypt
A model of the equinoctial sun latent in the configuration of the sarcophagus of Khufu's Horizon:
The sarcophagus in Khufu's Horizon is slightly skewed.
Its long external diagonal is 1/2 digit longer than the short external diagonal, so the long diagonal is precisely 1/4 digit longer than would have been the case for a perfect rectangle and the short diagonal is 1/4 digit shorter
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Mark Heaton
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Ancient Egypt
Well done.
Good reasons must, of force, give way to better.
Mark
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Mark Heaton
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Ancient Egypt
Taking your figures at face value without checking:
The bend is 0.11 metres lower than the height predicted in the model from Petrie's survey assuming Petrie's cubit of 20.68 inches as 90 cubits x 52.53 cm = 47.28 metres compared to 47.17 metres.
It must be remembered that if there was a change in plan then the level of 90 cubits would not have been a crucial design feature at the
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Mark Heaton
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Ancient Egypt
Thanks for that.
Just read Perring's survey as reported by Vyse
From Perring's survey data the north-south axis is very close to the centre line of the second antechamber.
I get a difference of about 3 inches.
Have I got this right?
Also the peak of the pyramid is above the second antechamber, about 3.6 cubits from the south wall by quick calculation.
Have I got this right?
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Mark Heaton
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Ancient Egypt
Hi Alex,
What you now propose is just the scheme that has already mentioned on this thread for which you raised the objection that it did not explain the upper slope of the Bent Pyramid, so you now want to focus on just the lower section to avoid your own question mark which is reasonable enough.
I agree that the corner angle of Bent Pyramid is slope angle of faces of Red Pyramid, but not q
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Mark Heaton
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Ancient Egypt
Just watched video. Interesting.
If there is no vertical passage in the Great Pyramid then perhaps the vertical shaft is part of the proposed stellar observatory.
I am trying to imagine what what one would see through a vertical shaft, presumably stars at 60 degrees from the pole if stars are imagined as on the surface of a sphere or hemisphere concentric with the earth, so would any such s
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Mark Heaton
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Ancient Egypt