Well done Waggi
Your model is an elegant model of the volume of a sphere with a diameter of 2.5 cubits (70 digits).
I calculated the geometric model in digits to a hundredth of a digit then rounded to the nearest fraction with no more than 16 divisions per digit then converted to British inches for comparison to the measurements of Petrie and Smyth:
I rounded Petrie's cubit of 20.632 inches for the granite King's Chamber to 20.63 inches as there is no significant difference.
The model of the interior is prior to the lid and rebate for the lid.
The internal area is said to be equal to a circle with a diameter of 2.5 cubits and the internal diagonal is 4 cubits.
The cubit was divided into 7 palms and 28 digits as 4 digits per palm according to I.E.S. Edwards.
The internal depth has to be 2/3 x 2.5 cubits = 46.66 digits for the volume of a sphere with a diameter of 2.5 cubits.
I used the pi approximation 22/7 in view of the 22/7 model of the exterior.
I calculated the model as:
105.94 digits X 36.34 digits X 46.67 digits are the theoretical approximations to Smyth's model for 22/7 on rounding to 2 decimal places.
A sphere with a diameter of 2.5 cubits equates to precisely 179,666.66 cubic digits for Pi = 22/7
Internal length 105 digits plus 15/16 digits, (Waggi 106) model 78.05 inches, mean of Petrie and Smyth 78.00 inches, diference 0.05 inches
Internal width 36.33 digits, (Waggi 36.33), model 26.77 inches, mean of Petrie and Smyth 26.77 inches, diference 0.00 inches
Internal depth 46.66 digits, (Waggi 46.66), model 34.38 inches, mean of Petrie and Smyth 34.38 inches, difference 0.00 inches
The internal length and internal width are irregular lengths defined by the internal diagonal of 4 cubits which equates to 112 digits:
112 digits, model 82.52 inches, mean of Petrie and Smyth 82.47 inches, difference 0.05 inches
Mark
Edited 4 time(s). Last edit at 11/08/2019 01:09PM by Mark Heaton.