AS "Sqds don't require calculation... they require selection."
This is not what the texts say. In the RMP, the height and the base are selected and calculation of the seked is asked for. Then the answers to the questions are the calculations of the sekeds. If the seked were selected, then the questions would say "given a seked 5 1/4 and a base of 12, calculate the heigh
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Jim Alison
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Ancient Egypt
In the diagram below, ABCD is a 2:1 rectangle. BD is arced to the diagonal at point E. CE is arced to point F. Point F is extended vertically to the diagonal at point G. Point G divides BC into a golden section. Point F divides CD into a golden section. The horizontal line from point G divides AC into a golden section. If CB is taken as the ceiling of the descending passage of the great py
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Jim Alison
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Ancient Egypt
Re: sqd - 16 years ago
My concern is not so much with the use or non use of the seked expression as it is with the idea that if the slope was expressed in sekeds then there is no other meaning or expression of the slope. In the RMP, one of the problems dealing with sekeds says "Given a height of 8 and a base of 12, find the seked. What is sought is the seked expression of the half base. However, what is given is
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Jim Alison
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Ancient Egypt
Re: sqd - 16 years ago
The slope of any four sided pyramid may be expressed in sekeds. The height is given as one cubit or seven palms and the half base is given as whatever number of palms fingers and/or additional unit fractions are required to express the slope. This does not mean that the slope of the pyramid was selected because of the seked expression of the slope. This is particularly true since most of the p
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Jim Alison
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Ancient Egypt
Petrie gives the length of the sloping roof of the descending passage in the great pyramid as 4137 inches from Vyse as corrected for casing. Petrie also gives the total vertical height of the descending passage as 1849.2 inches, plus or minus one inch. Given the slope of 2:1 for the descending passage, the vertical height times the square root of five gives the sloping length. 1849.2 times the
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Jim Alison
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Ancient Egypt
The ancient Egyptians had a measure for the diagonal of a one cubit square (the double remen). They knew that the area of a square on the double remen was twice the area of the one cubit square and they used the diagonal measure to double the area of a square while retaining the shape of a square area. This is another example of ancient Egyptian awareness of the area of the two shorter sides bein
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Jim Alison
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Ancient Egypt
Lubicz says the last step of the solution, getting the side length of 6 after the side length of 8 has already been determined, is uncertain because of deterioration of the papyrus. The scribe arrived at the correct solution to the problem. However, the question alone (given a square with side 10, find the sidelengths of two squares in ratio 3:4 that have a combined area equal to the area of th
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Jim Alison
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Ancient Egypt
Kanga mentioned the problems in th Berlin Papyrus relating to 3-4-5 triangles. One of these problems relates directly to Pythagoras theory that the squares of the sides are equal to the square of the hypotenuse, and the sidelengths used in the problem are in the proportion 3:4:5.
The following text is from The Temple of Man by Schwaller de Lubicz pp. 143-144:
"We offer an example take
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Jim Alison
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Ancient Egypt
Hi Jon,
Your quotes from Rossi say that the Pyramideon was intended for the bent before the slope of the bent was changed due to structural problems. I think Rossi is really saying that the unproven idea that the pyramideon was for the bent supports the disputed theory that the bent was originally intended to be a straight sided pyramid. If so, then hopefully the same posters who have readily
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Jim Alison
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Ancient Egypt
Hi Jon,
Thanks for this info. I noticed that RMP 56 is a seked problem with a pyramid baselength of 360 cubits and a height of 250 cubits. The answer is seked 5 1/25 or five palms and 1/25th of a palm. This translates to 54 deg 14', which is oddly the precise angle for the lower part of the bent given by Perring, before the RMP was discovered and before sekeds were considered as a poss
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Jim Alison
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Ancient Egypt
Perhaps you can otherwise explain why the king's chamber in the great pyramid is 11.18 cubits high, the same phi factor used in my proposed construction of the bent. And of course the ratio between the slant height and the half base of the great pyramid is 1.618 to one, just to mention a couple of well known examples.
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Jim Alison
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Ancient Egypt
Based on his survey of the bent pyramid, J.S. Perring gave 54 deg 14' for the slope of the lower part and 42 deg 59' for the slope of the upper part of the bent. Petrie found the slopes of the bent to be variable. He reported measurments for the slope of the lower part of the bent ranging from 53 deg 44' to 55 deg 23' and measurements ranging from 42 deg 39' to 43 deg 2
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Jim Alison
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Ancient Egypt
Hi Jon,
The Orion correlation is usually calculated assuming a perfect fit between the first two stars of Orion's belt and the apexes of the first two pyramids. The result is the third star misses the apex of the third pyramid by about 49m west and about 20m south. Moving the originally intended apex of G2 to the north and the east would make the Orion correlation dramatically better, b
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Jim Alison
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Ancient Egypt
In H. R Butler's book "Egyptian Pyramid Geometry", he quotes M and R as saying that they measured the angles of casing blocks that were lying around the pyramid and found the angle to be 44 degrees. Butler also says that Robins Shute give 44 degrees from their photogrammatic study.
According to Petrie's survey, and I think Legon says that Dorner's survey confirmed t
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Jim Alison
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Ancient Egypt
Lehner gives sidelengths 220m, height 105m and angle of 43 deg 22 minutes. (1997)
Edwards gives sidelengths of 722 ft, height of 343 ft and angle of 43 deg 36 minutes (rev. ed. 1985)
Baines and Malek give sidelengths of 220m, height of 104m and angle of 43 deg 22 minutes (1980).
As far as I know, the sidelengths of 220m (420 cubits) are not in dispute. An angle of 45 deg would require a
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Jim Alison
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Ancient Egypt
Gillings gives the scribes calculation as follows:
The scribe writes 1 divided by 3 1/7 equals 1/22 divided by 1/7.
1/22 is doubled to 1/11, producing: 1 divided by 3 1/7 equals 1/11 divided by (1/4 plus 1/28)
1/11 is doubled to 1/6 plus 1/66, producing: 1 divided by 3 1/7 equals (1/6 plus 1/66) divided by (1/2 plus 1/14).
The scribe writes this as:
1 -------------------------- 3 1
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Jim Alison
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Ancient Egypt
Hi Lobo,
You should have been a scribe. According to Gillings, fewer unit fractions and lower unit fractions are preferable, and yours wins on both counts. I am going to go back and look at the calculations and see if I can figure out any reason it was done the other way.
Jim
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Jim Alison
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Ancient Egypt
As far as I know, neither the shape of the scoop or the one-hekat measure is specified as cylindrical or right angled in RMP 38. It was my observation that the volume of a cylindrical container with a radius and a height equal to the sidelengths of a cube is 3 1/7 times the volume of the cube, meeting the specification of the question that the volume of the hekat measure is 3 1/7 times the volum
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Jim Alison
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Ancient Egypt
A hekat is a measure of volume defined as 1/30th of a cubic cubit.
RMP #'s 35-38 involve solving for fractions of a hekat.
In "Mathematics in the Time of the Pharoahs", Gillings gives problem #38 as follows:
3 1/7 times the container is required to fill the hekat measure. What is the volume of the container? To find the volume of the container, the scribe has to divide on
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Jim Alison
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Ancient Egypt
Kanga,
The Washington Monument was not built (or laid out) until approximately 70 years after the White House and the Capitol building, and it is not precisely on the NS axis of the White House or the EW axis of the Capitol building either. However, it is close enough that it appears to have been planned that way, and we know that is how it was planned, from the very beginning of construction
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Jim Alison
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Ancient History
Hi Pounder,
Butler adopts all of Petrie's measures as converted to cubits based on the baselength of G1 being equal to 440 cubits, and Butler adopts Petrie's orienation of five minutes west of due north for all north south and east west measures, based on the orientation of the first two pyramids. As a result, the west side of the third pyramid is 3 cubits further west that I have s
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Jim Alison
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Ancient History
Hi Wayne,
I just checked your finding that the distance from NE corner of G2 to the southern edge of G1, 110 cubits east of the SW corner, is equal to the baselength of G2. Given a 250 cubit NS distance between southern G1 and northern G2, and given a 500 cubit distance between mid south G1 and NE G2, the EW distance from the west side of G1 to east side of G2 must be 213 cubits, as indicated
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Jim Alison
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Ancient History
Hi Wayne,
I have not had a chance to look at this until now. Very impressive. I checked a few of your alignments with a sketch program and it looks good. I have not checked the math yet, but I will. I notice that the azimuth of the line from SW G1 to G3 is close to the G1 slope angle.
Jim
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Jim Alison
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Ancient History
Thanks for the links. I have wanted to review Cook's pages recently but I did not know his new address. Much appreciated.
Butler says that he thinks it becomes to complicated to analyze the intended dimensions of the siteplan unless a standard cubit and a standard azimuth is assumed for all of the pyramids. I do not agree with this. Even though the third pyramid measures 201.4 cubits us
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Jim Alison
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Ancient History
I have Butler's book and I think it is very strong. Some of his findings were discussed on Robin Cook's website which is not up anymore. Cooks old webpages can be accessed in the wayback archives but unfortunately most of the images are not archived and some of his data and explanations were on the images, which makes the archived pages hard to understand, even if you have a fairly go
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Jim Alison
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Ancient History
Is there any question that for the ancient Egyptians, South was up and North was down, as in Upper Egypt is South and Lower Egypt is North, and as in the Nile flows down to the North, etc, etc. Mentaka is the upper belt star in the sky and in the Sah representations. The sensibility of the modern Eurocentric view is that North is up. Krupp would have the upper star of Orion's belt in the N
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Jim Alison
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Ancient History
Hi Dave,
Nice pic - work it!
My calculation of a 5 arc second deviation in the orientation is as follows:
1 degree divided by 60 = .01666 for one arc minute
.01666 divided by 12 = .0013888 for five arc seconds
The tan of .0013888 is .00002424
.00002424 times 440 cubits = .010666 cubits
.01666 cubits equals .2 inches
If I am calculating this correctly, then the deviation pr
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Jim Alison
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Ancient History
Hi Jon,
Great graphics. Somewhat mind bending with the empty space of the chambers and passages being shown as solid (complete with shadows) while the solid masonry of the pyramid around the chambers and passages being shown as empty space.
I could not resist looking into your question about the significance of the height of the thick layer at the 35th course. Here is what I found:
1.
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Jim Alison
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Ancient History
Hi Dave,
`
There are a few errors. In his main diagram of his grid, in appendix 4 on p. 454, he gives the half base of the pyramid that is derived from his grid as 299.99 cubits. I know that this is a typo and it is meant to be 219.99 cubits but still...
Here is a another quote from the book:
"As far as the Great Pyramid's exterior was concerned, Petrie found errors that none o
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Jim Alison
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Ancient History
I do not know why Romer champions Spence either. He does spend a good bit of time discussing the length of time it took to build the pyramids, including Djoser, Meidum, the bent, the red and the great pyramid. I think some of his points and arguments in this regard are very good and very interesting. By the way, he gives 14 years for the construction of the great pyramid from start to finish (
by
Jim Alison
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Ancient History