I am updating on a new find with respect to the System B numbers:
Quote
Ossendrijver
“For Saturn: the height is 14;4,42,30, the depth 11;14,2,30, the difference 0;12”
These are sexagesimal numbers - the part before the semicolon is an integer and the part after the semicolon is fractional. For now let’s work on the integer portion of the height and the depth.
We have height of 14 against the great pyramids height of 280 (14 x 20) RC and depth of 220(11 x 20) for half the base-length, which is used to generate a right angle triangle for trigonometric calculations.
Now moving to the fractional part. The 14;4,2,20 height is organised in place value in descending powers of 60, so the 4 is 4 x 60
-1 or 4/60. Similarly the depth of 11;14,2,30, the 14 refers to 14/60. These reduce down into their lowest common denominator to 2/30 height and 7/30 depth. There is a feature of the core stones discovered by Zalewski and published in 2017 that forms what Zalewski terms an alpha triangle. Quoting Zalewski:
Quote
Zalewski
“The triangles with the base in the foundation of the Great Pyramid at Giza and their sides in its walls (I name them Alpha triangles) are visible in the four walls of the pyramid [21]. From mentioned triangles the most visible is the triangle located in the western wall, topped with a single stone. It is in the 19th layer of the stones, 16 m 65 cm high (Fig. 8b). According to the calculations the angle of all mentioned triangles in its top amounts 155 degrees. The length of its base is about 150 meters.”
Culminating at the height of 16.65m in the 19th layer, this alpha triangle would be formed on the face of the pyramid. If we fold it out flat, using the same 280:220 height:base of the right angle triangle that forms Khufu's pyramid, then the apex of this triangle would be 16.65 / (280/220) / 0.523748 (m per Royal Cubit) = 24.98 Royal Cubits in from the base. This allows us to use pythagorus theorem to calculate the length from base to apex along the face of the pyramid. This yields approx 40.43 Royal Cubits (the height of this triangle when laid flat). The base of the right angle triangle is half of the approx. 150m or 75m = 143.19 Royal Cubits. Using the same 20:1 scale as the integer portion which relates to the height and baselength of the great pyramid, reduces this ratio down to 2.02 (height) and 7.16 (depth) against expected values described above of 2/30 (height) and 7/30 (depth). Demonstrating that the first place of the fractional components are encoded on Khufu's pyramid as well. Ptolemy provides evidence that there was a source from Egypt, ancient in his time where 30 was used as the divisor in an astrological sense.
I have not found evidence of the remaining places of fractional values. The difference (0;12) in the Uruk text means 0 + 12/60 = 0.2 or reduced down into its lowest common denominator 1/5. The Queens Pyramids are thought to be approximately 1/5 of the size of Khufu's pyramid.
As such the key numbers for the exterior design of the pyramid are present in Uruk System B Tau zig zag function parameters, including the first place fractional values.
References:
Babylonian Mathematical Astronomy: Procedure Texts By Mathieu Ossendrijver pp 309-310
Ptolemy C., Tetrabiblos, accessed from [
penelope.uchicago.edu]
Zalewski, F., Petrographic Observations of the Building Stones of the Great Pyramid of Giza, Journal of Geological Resource and Engineering 4 (2017) pp 153-168
