The question I asked myself over and over again is -Why is Jim uisng 20.625 as the REC? but I couldn't amswer this question because I did not understand the Roman, Greek and Egyptian feet you kept writing about but fortunately I got a copy of Berrriman.
This is Berriman's Royal cubit
(3x3x3x3x3x3)/1000 x 4375/4374 x 20 x 99/70 = 25 x 990/1200 ( this supports the argument that the royal cubit can be either 28 of 25 units of measure.)
since the royal cubit most certainly is 25 x 990/1200 = 20.625
This is the JW and Berriman Royal cubit that I now subscribe to after spending months trying to figure this out.
This comes from the Egyptian foot of 11.666r inches /16 = 0.7291666r which is 0.729 x 4375/4374.The point being is that this foot is used to design the GP because it is Egyptian something that i really needed to confirm based on Berriman and I have done this.
11.6666r / 16 x 20 is the remen of 14.58333r inches.This is the remen of the Royal cubit which is 20 root 2 remen and root 2 is 99/70.
14.58333r x 99/70 = 20.625 this is Berriman's Royal cubit.
So that is the Egyptian foot, remen, and digit sorted for the Royal cubit.( you would not expect the Royal cubit to be designed against a Roman foot)
20 root 2 in this instance is 20 x 99/70 = 1980/70 = 28.28571 x 0.7291666r = 20.625
this is the Royal cubit attacked from virtually every angle decimally fractionally base 25 and base 28 the only missing element is 28.125 x 0.7333r = 20.625 (0.7333r being the eclipse digit)
the tricky bit of the REC is the Egyptian foot and Berriman gives it as [(35/27) / (16 x 9)] x 16 this 35/27 x 9 so it is 35/3 = 11.666r imperial inches
it is 315 / 432 and the suggestion of 3.15 Pi is raised
315/432 = 0.7291666r x 16 = 11.666r
Linking this to the Roman foot gives 11.666r x 4374/4375 = 11.664
0.729 x 1.00229 x 20 x 1.414286 = 20.625 where 0.729 is the digit of the Roman foot.
the bit that was tricky, more than tricky!! was the switch from Roman digit to Egyptian digit but I hope I have made the reasons for the transition clear.
Now for the Greek foot
This is the Roman foot x 25/24 = 12.15 inches.
This Roman foot is a misnomer because it is most certainly Babylonian.
and this is the other cubit calculated exactly the same way
(3x3x3x3x3x3)/1000 x 20 x 140/99 = 204120 / 9900
The only change in the calculation is that 0.729 is used as the Roman digit replacing the Egyptian digit and 140/99 replaces 99/70 as the root 2 approximate but this still agrees Berriman's interpretations of root 2.
The remen is 20 x 0.729 = 14.58 x 140/99 = 204120/9900 = 20.618181818r x 1760 = 36288.
This cubit is 28.2828282828r x 0.729 = 20.61818181818r
This is the real point i am making here. Berriman is giving us two options
One is 20.625 as 9900/480
One is 20.6181818r as 204120/9900 this is john Neal's cubit
i am trying to dig into the deisgns of the two cubits to see what is going on and I am saying that 0.729 does not fit 20.62 in any way, it fits 20.6181818r Neal's cubit.
If you multiply Neal's cubit by 176/175 you get 20.736 Michell's cubit, yet another reason for not accepting 20.6181818r as Royal.
It is very clear from the analysis that the Royal cubit is base 99 something i have been saying since i investigated Thom's work at Stonehenge.
20.625 x 1760 = 36300 and 20.625 x 1777.777r = 36666.666r
16000/9 = 1777.777r and 16/9 is one side of Eyptian Pi so the Royal cubit is multiplied by 16/9 x 1000. it really does not get any more Egyptian if it tried. The Royal cubit is Royal for this reason. It works in base 99 and base 100 and all the way to the top of the GP.
you are the guys who have been using these figures for years so If i have got this wrong let me know why, but i never felt like you knew why you were using those different feet.
i know why the Egyptians used 11.666r now
36666.666r / 11.666r = 3142.857143 one thousand units of Pi as 22/7 is the GP base
The height is 5833.333r inches / 11.666r = 500 and they used 500 because the GP framework is 2 x 22/7 so only 500 units is reuired to give 1000 pi in the base.
I know there are other Egyptian feet on offer but they don't do this so no thanks in advance.Neal was disparaging about Berrimans calcs in his Opus 2.
11.666r x 3 = 35 it is base 7
remember 35/27 in the above workings? It is 1.296296296r /16 x 9 = the egyptian digit.
Edited 1 time(s). Last edit at 22-Dec-19 16:41 by DavidK.