I am sure there are other numerical relationships understood by the architect of Khafre's pyramid but overlooked by the modern mind.
The question of how much the ancient Egyptians understood has often been considered in relation to what we know without considering the possibility that the ancient Egyptians may have understood more than we know.
I have discovered another equation which
by
Mark Heaton
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Ancient Egypt
Volume of Khafre's Pyramid
I thought you were agreeing with me when I first read your post.
height = h = 274
side length of base = b = 411
Volume = 3/4 x h x h x h = 3/4 x 274 x 274 x 274 = 3/4 x 2/3 x 411 x 2/3 x 411 x 274 = 3/4 x 4/9 x 411 x 411 x 274 = 3/9 x b x b x h = 1/3 x area of base x height
The volume is only 3/4 x h x h x h for the special case where the the rise of
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Mark Heaton
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Ancient Egypt
Please see page 94 of the 1885 edition of Petrie's publication on 'The Pyramids and Temple of Giza'.
'That the cubit was divided decimally in the fourth dynasty we know..'
''but having found the pi proportion in the form of the Pyramid, and in the King's Chamber, there is some ground for supposing that it was intended also in the coffer..'
M
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Mark Heaton
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Ancient Egypt
In response to Byrd:
Yes they did have 'decimal fractions'.
0.5 = 1/10 + 1/10 + 1/10 + 1/10 + 1/10
There is a cubit ruler in the Louvre which has a division of the digit into 10 parts which are decimal fractions of a digit.
But I actually wrote 36.5 rather than 36 1/2 (one over two) because it is simpler to write.
Anyone who ever picked up the ruler, who understood the ru
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Mark Heaton
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Ancient Egypt
Not really a problem .
My proposition is self-evident.
This is new evidence.
It is a fact that my model of the Bent Pyramid, based on Petrie's view of the sides of the base as 360 cubits, yields a circle with a circumference of 360 cubits with its centre at the centre of the base, precisely so.
Mark
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Mark Heaton
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Ancient Egypt
It was www.ancientcalendar.co.uk which I think I put on line for at least a year from 2012 until interest in my website diminished.
I'm fairly sure I posted about it on this forum, and certainly didn't debate it elsewhere.
A scientist said he thought it may be worth trying to re-construct my ideas without the proposition that the geometry signified 2770 BC.
I did use the dating
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Mark Heaton
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Ancient Egypt
To get back to source simply follow the chain of references.
Richard Parker was professor at Brown University and wrote much on astronomical texts, so read Parker's works (12 volumes) then the work of those he referred to.
Neugebauer pointed out that it is not possible to exclude a date of origin for the cycle 'say 500 BC' but wherever I first read comment on this matter I kn
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Mark Heaton
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Ancient Egypt
I suppose the ancient Egyptians were sure that the number of lunar months in 9125 days (25 years x 365 days per year) is greater than 308.5 and less than 309.5, but I am not suggesting that they knew how precise the number 309 is to reality.
The ancient mind may, however, have assumed that the number 309 is exact, but there is no reason it should be a round number, so the search for a very clo
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Mark Heaton
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Ancient Egypt
A division of the cubit into palms or digits has the potential for a symbolic model in either cubits or palms or digits.
The perimeter is 320 palms in the proposed model rather that 322 palms (for 16 x 7 cubits), so the irregular length and width yields a perimeter divisible by 40 palms.
Mark
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Mark Heaton
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Ancient Egypt
The floor is 111.5 palms x 48.5 palms in my model.
Mark
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Mark Heaton
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Ancient Egypt
Quite ingenious geometry:
Draw a rectangle 111.5 palms x 48.5 palms with a north-south axis of 111.5 palms and an east-west axis of 48.5 palms inside the floor area.
The axes divide the floor into 4 equal areas such that the axes divide the perimeter of 320 palms into 4 sections of 80 palms.
The perimeter is equal to 8 x 40 palms (compared to 8 x 1460 palms for the base of the Red Pyrami
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Mark Heaton
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Ancient Egypt
Thanks Hermione,
I got photocopies of Smyth Vol 2 and Petrie's 1883 work by just asking the British Library. Smyth's work didn't turn, so after a while they sent it me again only for the previous one to turn up.
It wasn't expensive.
Before I knew little about computers, so very little, I borrowed a printer, having typed up my monograph over many months, and printed out
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Mark Heaton
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Ancient Egypt
Thanks for that.
The notion that the Egyptians had two calendars is a notion.
Mark
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Mark Heaton
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Ancient Egypt
In response to Byrd:
Many Egyptologists start with the notion of Sirius, but Sirius was merely a marker of the solar year.
It is true that its cycle happened to be 365.249 days or 365.251 in the Pyramid Age (rather than the solar cycle of 365.242 days), but this is only known from modern astronomy, and of no help except in the minds of Egyptologists who somehow suppose it was. Observation
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Mark Heaton
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Ancient Egypt
This new topic raises the question:
Is the Egyptian calendar latent in the design of the Red Pyramid?
Step 1
It occurred to me that Petrie's mean cubit of 20.68 inches for the Southern pyramid of Dahshur (the Bent Pyramid) and its satellite pyramid, as detailed on page 32 of Petrie's 'A season in Egypt 1887' may be applicable to 'The Great Pyramid of Dahshur
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Mark Heaton
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Ancient Egypt
Hi Robin,
I was just replying to Don really, but I welcome your interest.
I will start a new topic on 'Egyptian calendar in the Red Pyramid?'
Regards,
Mark
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Mark Heaton
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Ancient Egypt
The first antechamber of the Red Pyramid, below the peak of the pyramid, is a model of the base square of the Red Pyramid.
The axes formed by the diagonals of the pyramid divide the perimeter of the antechamber into '8 x 40' palms.
The arris edges below these diagonals have a length of 360 cubits.
There is a division of 360 degrees into 8 x 45 degrees in this model.
The peri
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Mark Heaton
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Ancient Egypt
No, is the short answer.
The slope of the Red Pyramid is the same as the Satellite Pyramid of the Bent Pyramid in my model.
The satellite pyramid has a skew relative to the Bent Pyramid, but at the mid-point it is 99 cubits.
The base of the Satellite Pyramid has a side length of 100 cubits.
The height of the Satellite Pyramid is not 100 cubits (Petrie).
I proposed a height of less
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Mark Heaton
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Ancient Egypt
I think Petrie should have noticed that the gable height is not 38 inches at a glance.
It is quite easy to see a difference between 38 inches and 62 inches especially for a surveyor.
Petrie should have considered whether the wall height was wrong or the gable height was wrong, but chose to assume both were correct by supposing measurement from a point beneath the floor which is bizarre bear
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Mark Heaton
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Ancient Egypt
Error upon error.
I think I estimated the height of the gable on Bezoni's illustration as about 6 feet (72 inches) last night, so about 3.5 cubits, not 76 inches.
This morning it looks to me like the height of the top corners may have been measured as 17 feet 3 inches (207 inches) not 19 feet 3 inches (231 inches).
Is there a typo in survey report of Vyse who worked in conjunction wit
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Mark Heaton
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Ancient Egypt
Another excellent guide by Keith Hamilton.
With regard to my model of the burial chamber:
The gable of a wall is the triangular shaped section at the top of a wall with the peak of the triangle at the height of the ridge of the roof, so we only need to know the height of the gable and the width of the wall to determine the slope of the roof.
I had relied on Petrie's reported height
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Mark Heaton
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Ancient Egypt
That's interesting that you have a relation to volume from what appears to be a constant angle, or at least very close to a 1 in 2 slope for different pyramids.
I aim to show that the volume of Khafre's pyramid is encoded in the burial chamber, but can't yet see how this might be related to the length of the passage or the cross-sectional area, so if you have anything on volume
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Mark Heaton
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Ancient Egypt
Thanks for your input to my topic.
Mark
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Mark Heaton
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Ancient Egypt
The beauty of my alternative model of Khafre's pyramid, right or wrong, is that it shows that there is no need to be concerned about whether the side length of the base was 410 or 411 cubits if it is accepted that the intended slope was a rise of '4' for a run of '3', but you will have to be patient until I can get round to writing up my research which only began a few we
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Mark Heaton
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Ancient Egypt
Please see my post May 17 3.31 PM
I will not be changing the length of the cubit in my paper because there is no need to.
Mark
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Mark Heaton
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Ancient Egypt
I agree with you that it is ratios which are important, so it actually makes no difference to my model if the base of Khafre's pyramid was 410 cubits or 411 cubits because the height is 2/3 multiplied by the side length of the base.
I will be explaining my model for a length of 411 cubits because this is the only way that I can communicate with those who insist that we know that the cubit
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Mark Heaton
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Ancient Egypt
My models of Bent Pyramid and the Red Pyramid require a cubit of 20.65 inches, and now you point out the pyramid of Meidum has a cubit of 20.65 inches.
My model of the Great Pyramid also requires a cubit of 20.65 inches.
The length of the King's Chamber of the Great Pyramid is regarded as 20 cubits (560 digits) at the base of the chamber..
Petrie subtracted the length of tiny cracks
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Mark Heaton
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Ancient Egypt
I found 'Colonel H. Vyse volume 2 Operations at Gizeh' on line free in google books earlier today, and also the dimensions of the burial chamber of Khafre's pyramid in which it appears to me that the gable height of 38 inches is uncertain which is just as well because I had remembered the height incorrectly as 36 inches from Petrie in earlier posts:
PROPOSED NEW MODEL IS 410 CUB
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Mark Heaton
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Ancient Egypt
Hi Hans,
It was Piazzi Smyth according to a review by James Bonwick on page 68 of his book, but Piazzi Smyth was quite skilful in attributing theories to others such as John Taylor and Isaac Newton.
In this case he drew credence from Sir John Herschel who merely answered a technical question without promoting the idea that the age of the pyramid may correspond to the date when the lower dec
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Mark Heaton
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Ancient Egypt
Thanks for all your detailed replies, even though we have gone off my topic.
In answer to your question on my topic:
I am struggling to differentiate between what I can see in the design and what the architect saw in the design because my observations can be dismissed as a coincidence if the perimeter was designed to be 73 cubits as a representation of the cattle count.
Therefore, I am w
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Mark Heaton
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Ancient Egypt