0523

Proposed derivations of the Royal Cubit.


The measurements for the cubit rods range from 523.5 to 529.2 mm (20.61 to 20.83 in) in length and are divided into seven palms, each palm is divided into four fingers, and the fingers are further subdivided (Egyptian royal cubit).

Early evidence for the use of this royal cubit comes from the Early Dynastic Period, on the Palermo Stone, the flood level of the Nile river during the reign of the Pharaoh Djer is given as measuring 6 cubits and 1 palm. The use of the royal cubit is also known from Old Kingdom architecture, from at least as early as the construction of the Step Pyramid of Djoser in around 2700 BC.
The Egyptians were by no means limited to using the cubit as a measure, and a ratio would also be used, along with foot, mile, metres, and kilometres.
Example:
0.523m cubit
0.523×3=1.569m
Also equal to
5’ 2.36”

A gnomon (as described) would be used with a variation of 0.0145°/0.0392°/day. Over the distance of 1km, the diagonal would equate to 0.962 with a perimeter of 2km.

Using a pinhole gnomon making measurements during the year at 1.0145°/day and 5.32/year adjusting for tilt in that month. The measurement for gnomon would probably be made in the construction area, visible markers 1km apart were readings would be taken. Each degree marks 68 days (2.289 months).

7.155° tilt=0.0392°/day
0.962=gnomon 1km
1.0145°=1÷(360÷365)/day

These numbers are also linked to the Devil's Quoites, Devil's Arrows, Gravrins, and Orion, but only after construction had begun. The number 1.91264 also appears in the Thornborough henge. In the conjunction of the planets Jupiter and Saturn at Thornborough henge, the number 1.91264 from °/km appears and has been suggested that the Egyptians arrived/returned at a later time to adjust this.

The area of the ellipse holds no connection with these used on Giza pyramids and is used only to connect peaks, ratio, and golden ratio. When using the angles associated with the Sphinx and a quadratic equation, an equation that is a progression of coordinates and gradients is used, this equates to two numbers, using these two and multiplying by 10 gives.

33x² + 14.61x - 4 = 0
x = 0.19121
x = -0.63393
×10
1.9121 and -6.3393 are produced.

A link with the ratios also appears here, Khufu’s pyramid ratio at 6.384 is the nearest.
(This error 0.045 +1 equals degrees per day).
Because they at this point used errors to three decimal points, then 0.523 or 1.912 would be the number used.
A gradient is a (change in y-coordinate)/(change in x-coordinate), using numbers from Nabta Playa. Two sets of coordinates are produced, and numbers or primers are used producing gradients. To achieve the higher numbers, the central stones were also used. The clockwise numbers were adjusted to produce gradients, and a (3,3) introduced, further calculation suggests the use of cubed roots.

221/22112
21/2112
(22112-2112÷221-21)

Gradient slope
(22,112−2,112)÷(221−21)=100

Angle of inclination 269.427°
Ratio 1000:1
(24,112−2,112)÷(221−21)=110
(32,112−2,112)÷(221−21)=150

As shown, there is no direct correlation between π and φ inside a circle but increasing the radius to 9πφ then the slope equals 45.747 units @ 45°. The following are produced from a triangle with these units.

Area = 523.21736
Perimeter = 110.44518
These numbers then connect to a royal cubit and Nabta Playa.

With this, the older structures ratios suggest they didn’t use radians (i.e., 360÷57.297=6.283) as a ratio but instead chose alignment vertically north at maximum tilt, of these the Red Pyramid shows signs of being aligned to a set date which has appeared before but it is in better condition then the Bent Pyramid which also shows signs of being aligned but to an earlier date. The Bent Pyramid could be suggested that it is aligned to maximum tilt with the connecting Satellite Pyramid showing signs of a date, about 4°=2580+16, width of path around at 43m which when converting into 4.3 as if degrees equals 2773.
The Bent and Red pyramids were constructed under Sneferu 2613 bc and show signs of being darkened similiar to the Black Pyramid, which was constructed from a rock formation already that colour. Djoser and satellite pyramids are offset by 3°/4° while others are aligned to maximum tilt.

Ratios
Pyramid of Djoser ratio=7.37
Red Pyramid ratio=4.4
Medium Pyramid ratio=5.62
Bent Pyramid ratio=7.24 variable
Satellite Pyramid ratio=8.12

From the Bent Pyramid, an angle of between 19°/21° from the north and a distance of 20km meets with the Giza Pyramids. From the step pyramids to the aligned pyramids occurred around Sneferu time, although the construction process remained that of a step, a different application was made on Khafre’s pyramid with construction in layered phases which was also applied to some of the Queen’s pyramids. 

The Ancient Egyptians show signs of favouring connection with structures followed by alignment, whilst considering the location lastly, although there is signs of an underlying plan for the Giza site and other pyramids which is based on the speed of light. Ratios are favoured more but links from one ratio to another even more, once a location is chosen and aligned and foundations laid as long as a block is inside of tolerance it would be used somewhere in it's construction, set measures by a stick of a certain height would be used, this would keep tolerances in line.

Use of the cubit as 0.523m arrived around 2700 bc and was probably chosen with its link to astrological objects and direct link to a 45° triangle. The connection between the cubit and π is 16 cubits÷5π, and this would then favour π from the φ.

(0.523×16)÷(3.142×5)=0.532

Notes
Egyptian terms used in measurement.
Peremus is the height of an object.
Ukha-thebet is the length of an object.
Seqed measures the slope of an angle.


Royal Cubit (continued..)

Further to using a quadratic equation on a gradient plot line, an equation of a straight line can be used, y=mx+c on coordinates points x,y.
Again, using the numbers derived from Nabta Playa, adjusting for x,y.
(21,221), (2112,22112)
y = 10.46x + 1.14

m is the gradient of the line, and c is the y-intercept where the graph crosses the x-axis. 1.14 is a point on the x-axis with a slope of 10.46x. In construction, a slope would be any side, not at 90° with the building surface. Coordinates could be used to define this along with angle and distance.

(Interestingly, 10.46 is 20 cubits, and 20 cubits length is a common measurement for not only Khufu's and his queen's tomb but other tombs that used similar ratios)

The connection between the cubit and π is 16 cubits÷5π, or

(0.523×16)÷(3.142×5)=0.532 

(0.532×5π)÷16=0.523

Multiplying this by ×10 equates to 5.32 and equals measurements/year.
Using 160×(50÷2) in a 45° triangle, the area equates to 1414.21356 with a perimeter of 328.41599.
In the same way, Khufu's pyramid ratio can be increased in the same way to achieve its ratio.
160÷(50÷2)=3.2×2=6.4
The area can be defined as
=1000√2
The perimeter can be defined as
=a+b+c
1÷ ³√(328.41599) with the following added, multipled by 2 connects with Mintaka separation distance from 0° =0.289°.

This number ÷10 +1 connects with daily measurements throughout the year 1.0145°.
On a 45° triangle, accurate to 3 decimal π can be defined as (eliminating √(2)).
45°=π÷4
((10÷4.5)÷√(2))×2
or (9×π)÷20=√2 

Interestingly, from the article 'Glaner Braut', a Neolithic grave built about 2700 bc in Germany, it is shown that 1985+20+3600=6562.

This number is made up from the year of maximum tilt, maximum tilt, and one hour in seconds. The reciprocal of this number is equal to the royal cubit plus one.

(1÷0.6562)=1.523

=1+0.523

In that article, it was used to define an astrological object to be one second measurement away at maximum tilt.

Cubit

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