The explanation of the Egyptian mystery concerning the fine-structure constant (137.035999935 Kinoshita) using NIST values:
Let c = speed of light=299792458 m/s
Let h = Planck's constant=6.62606876*(10^-34) Js
Let E = Permitivitty of vacuum (electric constant) = 8.854187817*(10^-12)
Let e = elementary charge=1.602176462*(10^-19) C
Let Beta = .37 (https://webphysics.iupui.edu/251/251Sp97GFApr28.shtml)
Using the form for derivation of Pythagorean tetrakys(1 2 3 4=10)
In this case E=8.854187824*(10^-12)
Popular knowledge says that the Egyptians had a crude value of Pi as 3.16.... however some say that the Egyptians had a more
accurate value built into the Cheops pyramid : base leg divided height=Pi/2. But the fine-structure form of the tetrakys shows a deeper meaning relating to the Cheops construct dimensions:
Using actual field measurements: 763.81/486.2560047
Note that to create the exact value of the tetrakys (10) Pi/2 is close but the actual field measurements of the Cheops pyramid are exact.
This tells me that the Egyptians did not use the Pi form as reference to dimensioning but instead used the fine-structure constant form which suggests that the Egyptians were familiar with the exact values (9 decimals) of the elementary charge e; the Planck constant h; the speed of light c; and the permitivitty of the vacuum E. There is no way that this could be a coincidence.
PS: Coincidence or not? The Egyptian pantheon of Gods has exactly 37 total.