OK let me explain
I took the quote out of context so my comment in not relevant but the misleading part is this.
20.62 and 0.729 do not go together because 20.62 only factorises as 2 x 1031 and this is very clumsy and inelegant.
0.729 as I say is 3x3x3x3x3x3/1000 and this is beautifully balanced so just multiply by 2x2x2x2 to get the Roman foot.
Multiply by 2x2x5 to get the Remen of 14.58 imperial inches. the imperial inch is the unit that holds everything together.
Now the cubit is then 14.58 x 140/99 and this version of root 2 is the 5 and 1/2 sekhed x 10/9 again very elegant.
The key rule we should all be aware of is that the square 9 becomes the circle 10 when pi is 22/7. This rule has to be followed. So 360 becomes 400 and the square 360 and circle 400 are the wrong way round if you get my meaning here.
Berriman (long after Griffith) suggests that they used 99/70 and 140/99 as root 2 both versions being root 7 and 11 as is the 5 and 1/2 sekhed and it is important to stay within this Egyptian framework.
When you say no point in expanding the decimals you are missing another rule in that all the numbers are fractions they did not do decimal points.
So the cubit is 14/11 x 10/9 x (3x3x3x3x3x3)/1000 x 20 = 2041200/99000 ( 20.625 is 9900/480) They are designed to work together.
This is a very different cubit to 20.62, one that complies with all the rules and is incredibly elegant and highlights the base 99 construction of this cubit discovered by John Neal and Michell.
It is 20.618181818r and this notation is very poor once the design is drilled into.
There is no room for error in these designs and talking about a number almost being another one is just plain wrong because 9801/9800 is hidden between the two versions of root 2 and is MC's Mr Dial's signature. Have you seen his Phos calc?
Once you know it is there deliberately, everything you thought you knew about the AE changes.
The correct cubit to use with 0.729 is
0.729 x 28.282828282828r = 20.618181818r
28.282828282828 is 20 root 2 being 1.414141414r
So Griffith was absolutely wrong numerically but theoretically correct.
20.62 / 0.729 = nearly 20 root 2 = 28.28532236 but this has to be converted to a fraction using base 7 and 11
To get 20.625 use the methodology above but use 0.729 x 4375/4374 as the digit.Yet more Dial magic.
4374 is 2 x 3 to the power 7
4375 is 5 to the power 4 x 7.
We have to chisel our way through the numbers to understand what was going on.
I hope you don't think I am being rude or critical because i am not. I misunderstood your article because I skim read it. the fact is there are not many who would understand these subtle numerical distinctions but you MC Thinkitover and Jim W certainly do.
I think we all have a duty of care with our findings and should work together because alone we will never get to the bottom of these fabulous systems.
I am promoting Berriman as a point of reference for Metrologists but only looking at units of length. Obviously he has his sources such as Greaves and I would imagine Petrie. So using his work is a very powerful reference tool.
Petrie suggested 20.611 for his cubit and since 10/9 is 1.11111r logically 20.611111r is the relevant cubit length.
20.6111r x 160/159 = 20.740740r the cubit that holds for his second determination.
These values are elegant and in compliance with Berriman's rules. That is all I need to say about them, other than 20.740740740r / 1.4141414141 = 14.666r my eclipse cubit( Discovered at Stonehenge by using the work of Thom).
Edited 4 time(s). Last edit at 22-Dec-19 10:56 by DavidK.