Hi RLH
RLH Wrote:
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> Hello All
>
> I was wondering if there was a way for the AE to
> have solved for diameter with a known
> circumference without using (22/7 = pi).
Yes there is, G1 demonstrates the process. (shown below)
> The key to what I came up with is 28/33. I’m not
> aware of them using this in any EMP’s but then
> AFAIK none of them required finding perimeter or
> circumference.
The process is based on the values of the 5 1/2 seked 11 run:14 rise.
> In my drawing I have on the right side the value
> of 37 5/7 (blue) for circumference so to find
> diameter I get.
>
> 37 5/7 * (28/33) = 32
> 32 / 8 = 4
> 4 * 3 = 12
> So 12 is the diameter.
Are you aware that you started with a value of pi (37 5/7 / 12 = 22/7). Actually 28/33 is (14/11 * 2/3) the values of sphere (28) to cube (33) surface areas.
<[
www.hallofmaat.com];
Surface area of sphere side^2 * 14/11 * 4 = area times 4 = surface area of sphere, translating surface area of the sphere to surface area of the cube 14/11 * 2/3 = 28/33 sphere surface area divided by 28/33 equals surface area of a cube in the same ratio as the seked circle and square.
Volume of sphere Area = side^2 * 14/11 * 4/3r = volume 4/3r * area
for translating volumes of spheres to cubes (14/11^2 * 2/3)
> For the GP I have.
>
> 440 / 3 = 146 2/3
> 146 2\3 * 8 = 1173 1/3
> (1173 1/3) / (28/33) = 1382 6/7
>
> So the circumference of a circle that fits the GP
> base is 1382 6/7 cubits
>
> Now taking the perimeter of the GP = 1760 cubits I
> get
>
> 1760 * (28/33) = 1493 1/3
> (1493 1/3) / 8 = 186 2/3
> (186 2/3) * 3 = 560 cubits
>
> And as 560 cubits is the diameter then 280 cubits
> is the radius.
>
> I welcome opinions on this good or bad and ask
> could this be something the AE might have used.
>
> RLH
>
The ratios of G1 indicates the circumference of the circle and perimeter of the square are equal, 1760 cubits, G1 states the radius of the circle, or height of the pyramid, divided by 7 times 11 equals the base of the pyramid or the side of the square giving the following ratios:
Radius 7 units to side 11 units 7/11
side 11 units to diameter 14 units 11/14 (run-rise of the 5 1/2 seked)
side 11 units to perimeter 44 units (4 * 11 = 44)
since the circumference is equal to the perimeter and the circumference is 44 units.
radius is 7 therefore the circumference to radius ratio is 44/7
the circumference to diameter ratio is 44/14 or 22/7
Evidently you noticed in the RMP and MMP the Ancient Egyptians worked primarily with areas and volumes and did not demonstrate any of our current concepts regarding pi. They did demonstrate that a unit squared divided by a fractional value will get the area of a circle.
G1 demonstrates that the diameter squared / 14/11 = area of circle or side squared * 14/11 = area of circle.
Regards,
Jacob