Hi Mark,

Thanks for the post.
Mark Heaton Wrote:
-------------------------------------------------------
> Petrie did not think the palm was divided into 4
> digits so he overlooked the fact that the
> perimeter of the long walls of the King Chamber
> not only corresponds to the circumference of a
> circle with the length taken as the diameter of
> the circle, but also corresponds to 1760 digits
> with 5 courses of 64 digits to the footing of the
> floor and a length of 560 digits.

<[www.ronaldbirdsall.com]; sections 140 141, I understand Petrie's dilemma regarding the cubit, palm and digit, but this problem is easily resolved by the use of fractions, in lieu of decimals he used. Fractions are clearly capable of explaining the dichotomy which bothered Petrie.

>
> This hypothetical circle is a 1/28 scale model of
> the size and shape of the intended dimensions of
> the Great Pyramid, so the height of the pyramid
> was intended to have a height of 560/2 cubits as
> the radius of the circle and the perimeter of 4 x
> 440 cubits was intended to be equal to the
> circumference of the virtual circle which equates
> to 1760 cubits as calculated from the pi
> approximation 22/7.
>
> It follows that the King's Chamber Circle is a
> model of the exterior on a scale of 1 digit to 1
> royal cubit because there are 28 digits in a
> cubit.

Where you see circles and spheres I see squares and rectangles that also represent circles. The Kings Chamber. width of 10 cubits, (70 palms, 280 digits) is 1/176 G1 perimeter,
The length of the Kings Chamber is 20 cubits, (140 palms, 560 digits) and is 1/88 G1’s perimeter.
The height of the Kings Chamber is 11 + 1/4 + 1/7 + 1/28 or 11 3/7 cubits, (80 palms, 320 digits) (measured from the base of the block wall) and is 1/154 the perimeter.
Therefore adding 1/154 + 1/154 + 1/88 + 1/88 = 1/28 the perimeter of G1 is the perimeter of the long walls in the Kings Chamber. In cubits the perimeter of long walls of the Kings Chamber is 11 3/7 + 11 3/7 + 20 + 20 + = 62 6/7 cubits (440 palms 1760 digits) and is 1/28 (one digit) the 1760 cubit perimeter of G1.

Being there is no mention of pi in any form found among the Ancient Egyptian archive material this possibly demonstrates how by the use of the 5 1/2 seked the Ancient Egyptians were able to achieved pi like results in the form of 3 + 1/7, using the 14/11 rise-run ratio of G1. Also demonstrating how it was possible for the Ancient Egyptian to attain the pi correlation Petrie’s observed between the North Wall perimeter and the length of the Kings Chamber. 62 6/7 cubits / 20 cubits = 3 1/7, and regardless of what we may think regarding the Ancient Egyptians use of pi. The available evidence indicates they were not cognizant of pi in any form, but were never the less able to achieve pi like results in G1 without the use of pi.

Perimeter of G1 1760 x height 280 = 492800 the surface area of a hemisphere radius 280 (if pi = 22/7)
492800 x 1/2 = 246400 area of circle radius 280,
246400 x 11/14 = 193600 = 440^2
Just as 1760 cubits x 28 = 49280 digits.
1760 x 7 = 12320 palms
12320 x 2 = 24640, 24640 x 2 = 49280

G1’s architect is unknown, but circumstantial evidence suggests that it was Khufu’s vizier Hemiunu, who in his mastaba G-4000 states G1 was designed against a cubit of 7 palms, 4 digits.
[www.researchgate.net];

> The niche in the Queen's Chamber shows the
> division of the cubit into 4 parts with 4 corbels
> on either side of the chamber reducing the width
> from 3 cubits to 1 cubit.
>
> The roof of the Grand Gallery shows the division
> of the cubit into 7 parts with 7 corbels on either
> side of the gallery reducing the width from 4
> cubits to 2 cubits.
>
> The division by 4 and a division by 7 means
> implies the cubit probably had 7 times 4 divisions
> as apparent from surviving cubit rods.

Various physical specimens of cubit rods with 12, 24, 27, 72, 180 and 360 subdivisions on the rods at Turin Museum, not just 7 palms and 28 digits to a rod.

>
> In my monograph on the Grand Gallery I pointed out
> that the length of the cubit apparent from the
> interior is incredibly close to the cubit apparent
> from the exterior which could have been achieved
> with 2 master stones 10 cubits in length.

Based on Petrie’s statements I would contend the exterior and interior cubits were intended to be the same, with the differences stemming from building errors that inevitably occur during construction on a structure the scope and magnitude of G1.
<[www.ronaldbirdsall.com]; of section 141 of The Pyramids and Temples of Gizeh, W.M. Flinders Petrie, 1883: “The values of the cubit and digit, found in use in the cases mentioned in this chapter, agree remarkably closely with what has been already worked out. For the cubit I had deduced (Inductive Metrology, p.50) from a quantity' of material, good, bad, and indifferent, 20.64 ± .02 as the best result that I could get; about a dozen of the actual cubit rods that are known yield 20.65 ± .01; and now from the earliest monuments we find that the cubit first used is 20.62, and the mean value from the seven buildings named is 20.63 ± .02. Here, then, by the earliest monument that is known to give the cubit, by the mean of the cubits in seven early monuments, by the mean of 28 examples of various dates and qualities, and by the mean of a dozen cubit rods, the result is always within 1/50 inch of 20.63. On the whole we may take 20.62 ± .01 as the original value, and reckon that it slightly increased on an average by repeated copyings in course of time.”

Based on all available evidence, I can find no reason to disagree with Petrie's assessment of 20.62 ± .01 being the original value for the cubit.

>
> These stones could have been made very square and
> moved around the base of the pyramid. The very
> same stones could then have been used to mark out
> the King's Chamber at every level of the chamber.
>
>
> It would then have made sense just to leave the 2
> master stones in the top course of the King's
> Chamber. There are in fact two such stones in the
> top course of the King's Chamber, and these stones
> define the width of the chamber at the top.
>
> The east side of the pyramid was probably built
> first according to Maragliogio and Rinaldi. If so
> the best estimate of the length of the cubit is
> the length of the east side divided by 440 cubits.
> All the other sides may be very slightly different
> than 440 cubits in the attempt to make a square.
>
> If the faces of the 2 stones on the ends are not
> perfectly flat, or were not fitted together
> perfectly, then this might add up to 1/25 inch for
> each length of 10 cubits or 1/250 inch per cubit,
> so if the master stones had a mean length of
> 20.610 inches then the cubit apparent from the
> base square may be as much as 20.614 inches.
>
> The best estimate of the cubit inside the pyramid
> may prove to be the aforesaid so-called master
> stones which should be measured for length near
> the top and bottom of each stone as well as the
> mid point.
> I would expect all 6 measurements to be in the
> range 206.00 inches to 206.15 inches if these were
> the master stones because a length of 10 cubits
> apparent from the east side is 206.08 inches from
> Petrie's survey and 206.15 inches from Cole's
> survey.

<[www.ronaldbirdsall.com];
Petrie measured mean the dimensions for the Kings Chamber Petrie for the North wall at 412.40, and 206.29 for the East wall, South wall 412.11 and West wall 205.97. The height of the Kings Chamber Petrie noted in section 56 after the math gives 235.3 ± .6 margin of error.

Actually a few bits of information within G1 showing Petrie’s assessed cubit length can be verified by using fractions and the dimensions of G1’s architectural details found in the Kings Chamber and Grand Gallery and the bronze cubit rod Specimen #4: Turin Museum Catalog #6349. Which brings us back to the questions posed in my opening post. Given the myriad of hypothesis and opinions regarding measurements of the Ancient Egyptian G1 Pyramid having been authored, ask yourself this question: what evidence leads anyone to believe or assume any surveyed dimension are the error free intended dimensions of G1 by Ancient Egyptian builders?

Jacob