especially the last line after my puny effort. The point here is that the decimal numbers are actually all Egyptian has you have made so clear but to our metricised brains the only significant number is 9.87654321 it stands out like a sore thumb. So i can use metric numbers and you know what i am actually using.
> 1.111111111 ........1 + 1/9...10/9...9/10 = 1/2 + 1/3 + 1/15
> 1.571428571 .........1 + 1/2 + 1/14...11/7...7/11 = 1/2 + 1/8 + 1/88
> 6.285714286 square..6 + 1/4 + 1/28...6 2/7...7/44 = 1/7 + 1/62 + 1/9548
> 6.984126984 circle. 6 + 1/2 + 1/3 + 1/7 + 1/126...440/63...63/440 = 1/7 + 1/3080
> 8.888888889 square..8 + 1/2 + 1/3 + 1/18..80/9....9/80 = 1/9 + 1/720
> 9.87654321 circle...9 + 1/2 + 1/3 + 1/24 + 1/648...800/81...81/800 = 1/10 + 1/800
Yes I know they can, I don't know your intent for this little exercise there but here for the numbers you posted are the Egyptian fraction, fraction and reciprocal in bold followed by the reciprocals Egyptian fractions for the each of the decimal figures which can be any designation can be radii, diameter, circumferences of circles, side lengths or diagonals of squares, or they can be arcs, straight lines or any other designation of the mathematical world. Without proper context the unit fractions are sometimes hard to calculate. The only thing these numbers can't be is irrational. '
they are infinite rationals
dividing them all by 10/9 gives
In this sequence 6.285714286 is multiplied by the seked 14/11 to give 8 - your calculation.
When these numbers are multiplied by 10/9 5.657142857 becomes 6.285714286.
5.657142857 is the inscribed square and to get the circle multiply by 10/9.
The point being the base number within this system is 1.1111r or 10/9.
In terms of hard evidence I am looking for Egyptian ratios reconciling to 6.285714286 and 8 and 1.2727272r the sekhed.
For me the really hard evidence comes from the monuments so once the soft system based calcs are done they can be tested against the actual monuments.
The first part of the analysis i have used is from Stonehenge and an anlysis of the Harris and Stockdale megalithic foot at SH.
I have to be careful what I say to you because this is clearly not Egyptian but it can be interpreted as such.
These are the units being used
1.272727272r x 1.1111 = 1.414141414r this is 140/99 and is the sekhed x 10/9.
1.8 / 1.272727272r = 1.414285714 this is 99/70 and is 18/10 divided by the sekhed
They were discovered at SH but can be translated using fractions which is what i had to do to understand what was going on.
The next unit being used is 1.414285714r x 10/9 = 1.571428571 x 4 = 6.285714286 as a four sided square and multiplying this by 140/99 gives a parallel larger square of 8.888r units which it must do to obey your rules with a radius of 10/9 as it is 80/9.
Multiplying it by 10/9 gives the external circle as 9.87654321 and this reverts back to your model by changing 10/9 back to one.
The reason 9.87654321 is important is when calculating the area of a circle using the Egyptian method.
Using a diameter of 10 the caculation is 10 less 10/9 or 1.111r
This is 8.888888888888888888888r x itself for the area = 79.0123456789
Divide this by 9.87654321 to get 8 just the same as for the square.
So the base 10 diameter produces a unit 8 area circle.
This is why i got excited about your sekhed disclosure because is rounded off the SH model but instead of investigating the Egyptian implications i went back to SH for a few weeks. Now that i am looking at the Egyptian calculations I realise an apology was required because i insinuated they must have used 22/7 when clearly they do not have to.
This unit 1/9 can be expanded to 1/900 or 0.0011111r and it reveals how the solar days can be interpreted.
If the base is 366.666r solar days or 366.666r x 24/25 as 352 it reveals everything about the relationship between Thom's measurements and the imperial.
366.666r is the imperial
362.666r is Thom as x 272/275.
366.666r / 0.00111r = 330000 usng Pi as 1760/560 at SH
362.666r / 0.00111r = 326400 using Pi as 1632/520 at SH
difference is 3600 or 60 x 60.
So to get a cubit it is solar days /17.6 and to get to base 33 it is solar days / 0.00111r
Im my book i write about making the 'quantum leap' which is the change in mindset required to understand Thom's work. The same applies to Egypt.
i am not saying that the calcs i have put up are Egyptian but they do comply with the rules required to make them so.
The fact that the metric unit being used is 9.87654321 will ring some bells.
For followers of Michell's canon 352 solar days / 0.001111r = 316800 and 330000 - 316800 = 13200 the 24/25 ratio.
Edited 3 time(s). Last edit at 26-Jun-18 10:59 by DavidK.