Anthony wrote: " I have always had the idea that Khafre's structure will require as much "deciphering" as Khufu's."
In this you are quite correct, but I believe it is also true that both pyramids are decipherable using the same modality. Yes, you guessed it - the two-fold squaring of the circle.
The derivation I propose not only explains why there are two en
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L Cooper
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Ancient Egypt
Warwick Nixon wrote: "WE could simply be witnessing a lack of the Lasar precision that so many assign to the AE's pyramid building. There could very easily be variation of One Degree from side to side to side to side, not to mention within each slope...without it throwing off the overall 'effective' accuracy."
It might not throw off the general accuracy of the struct
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L Cooper
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Ancient Egypt
Jon,
I thank you for the Stadellman and Fakhry information.
If one looks at the Dorner survey - where he measures an average casing-stone slope of 44°44', but then computes the elevation of the entrance assuming a slope of 45° - one finds that there is then (what I consider to be) a significant difference of about 1 foot in the determination of the entrance elevation. I see this as be
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L Cooper
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Ancient Egypt
Petrie (in A Season in Egypt, 1887) states that his measurements were of the core masonry, and found the north and west sides to be 44°42 and 44°41' respectively, while he found the east and south sides to be 44°32' and 44°30' respectively.
He then states that the "mean" angle for the sides is 44°36' +/- 3', and follows this by saying that the "likely
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L Cooper
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Ancient Egypt
Hermione,
Forgive me. I will belabor this thread no more beyond this post, however I do believe you are misreading what I have said, and in fact are taking the opposite meaning from my statements.
You state, "The theory that the AE knew about pi has been aired on Ma'at on countless occasions", and that you are weary of this subject.
I have been as clear as I have been a
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L Cooper
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Ancient Egypt
Hermione wrote: "Have you come across this article?"
I first read it a while ago. I note that the author supports my statement regarding the 28 finger cubit rod, but then goes on to make an incorrect assumption - an assumption upon which the rest of his article is then based. First, let me quote him directly:
"How could the Egyptians have discovered the 3 1/7 value for p
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L Cooper
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Ancient Egypt
Hermione wrote :
"This, I'm afraid, is a glaring example of a straw man argument. What's been said on innumerable threads is that there is nothing to suggest that the AEs actually recognized that the fraction 3 1/7 or 22/7 was also the ratio of the relationship between a circle's diameter and circumference. To them, it was just a fraction."
Actually, 22/7 is the r
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L Cooper
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Ancient Egypt
Anthony wrote:
"That's probably because it is your preconceived conclusion that you will find it there. You hunt until you do."
Please accept a few comments to this remark.
First off, I did not begin my research from a "preconceived conclusion", as you have charged. I actually stumbled into it while working on a completely unrelated geometrical problem. I suppos
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L Cooper
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Ancient Egypt
Ronald wrote:
"I see the AE mainly as intuïtive builders, not as builders regularly using maths."
Up to this time my investigations have focused solely on the Khufu, Khafre, Bent and Red pyramids, but in all of these I have found that the design of each interior layout appears to be based on a squaring of the circle mechanism. The method used in every case is a relatively simple
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L Cooper
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Ancient Egypt
Ronald wrote;
"The "squaring the circle" arguments are a product of modern minds. One has to try to replace her/himself into the mind of the Ancient Egyptians. These people certainly did not think within the concepts of maths we have today. There also was simply no need to do so. I retain my view that you do not need much 'math' (what's in a name ?) to build ten
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L Cooper
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Ancient Egypt
As I mentioned in a thread earlier this spring, my bet is that the Queen's Chamber shafts each continue for 9.2 meters beyond the downslope face of the first "door", meaning that the shafts continue for about 9 meters beyond the downslope face of the second "door". This prediction follows from the gemetrical construction which I have proposed to be the design basis for t
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L Cooper
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Ancient Egypt
In an earlier posting made here, and in a letter I have sent to Zahi Hawass at the SCA address, I have expressed my hope that the new robotic exploration of the Queen's Chamber shafts will have the capability to send a fiber optic probe, or some such device, a distance of about 9.2 meters from the front surface of the first "door" in each shaft (i.e., from the "Gantenbrink doo
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L Cooper
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Ancient Egypt
Does anyone know the status of the new robotic exploration of the Queen's Chamber shafts that I believe had been planned to take place in February or March?
Many Thanks.
Lee Cooper
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L Cooper
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Ancient History
Hello Lobo-hotei,
You wrote:
Well using the same type of process, and the same example used for the area problem, you can find an approximation for the "squaring" of the circumference that is as accurate(slightly more so actually).
Yes, what you say is true - and I do not doubt that they did so at least as early as the Third Dynasty. The 28 finger division of the royal cubit i
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L Cooper
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Ancient History
Hi C. Wayne,
I truly appreciate your going to the time and trouble to construct the diagram in a CAD context. Excellent!
As I've said, the computations of the relative lengths in the protocol and diagram which I propose, when scaled to the actual size of the monument, with great consistency match Petrie's findings. This is the true test. If the CAD drawings do not exactly align,
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L Cooper
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Ancient History
Hello C. Wayne,
You wrote:
Do you agree that:
1. The CAD drawing of your "squaring the circle" plan I posted is accurate,
2. The CAD drawing of G1 posted by Gantenbrink is accurate,
3. The two drawings have incongruities amounting to multiple cubits, and
4. The builders of the pyramid used tolerances of less than 1/2 cubit.
5. Therefore, your plan does not fit G1.
If y
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L Cooper
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Ancient History
Hello C. Wayne,
Thank you for your post. In response to your questions:
First, the drawing from my website was done in Appleworks and it is not meant to provide, nor is it capable of providing, the kind of accuracy found in a well drafted CAD drawing. I am actually surprised that a comparison came out looking as close as yours does. No, the rubber meets the road in comparing the diagram&
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L Cooper
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Ancient History
Anthony,
As I stated in an earlier post, the main "cultural evidence" to support an AE interest in squaring the circle obviously lies in the Rhind Mathematical Papyrus (problems 41, 42, 43, 48 and 50). R. J. Gillings says of the scribe who wrote this papyrus that "his method allows him to find a square nearly equal to a circle, so that we can, "en caprice", as it we
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L Cooper
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Ancient History
C. Wayne,
No, I do not believe that the Pi (and/or Phi) ratio was - or could have been - a precipitating factor in the Egyptian pyramid design. You ask me to summarize why I say this, but rather than take up the time and space to do so here, it would perhaps be easier to just read through the introductory section at any of the web pages I list on these pyramids (http://www.atara.net/pyramids/)
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L Cooper
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Ancient History
Dave,
I respectfully also disagree that the pi ratio was "an important primary design factor" in pyramid design.. The appearance of Pi proportions in the Old Kingdom pyramids is, I believe, a byproduct - or a function - of what I suggest was the primary design factor - namely to have the design of these structures diagrammatically reflect the squaring of a circle both in terms of th
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L Cooper
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Ancient History
MJ Thomas spoke of the need to "figure out the sequence of the (Khufu) Pyramid's design" in order to make inroads into why things were placed where they were in this pyramid. Since I've developed some ideas on just such a sequence, I guess I'll throw in my two cents.
Although I haven't spent any time trying to unravel the reasoning for the design and placement of
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L Cooper
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Ancient History
MJ and Jon, thank you for your replies.
Jon, when you say that "the offset for the entrance of Khafre's Pyramid .......would appear to be wrong", are you referring to Petrie's result, Perring's, or both? I also feel that something may not be spot on here, and I'm curious to know what leads you to think so as well.
Thanks.
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L Cooper
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Ancient History
Petrie states that the axis of the Khafre Pyramid's upper entrance passage is 490.3 inches to the east of the pyramid's north side midpoint. Perring places it at 526 inches east of this midpoint. I know that Petrie considered Perring to be a bit of a bounder, but I am wondering whether there has been another survey of this pyramid which has remeasured this factor.
Anyone know more ab
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L Cooper
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Ancient History
