Clive Wrote:
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> MJ Thomas Wrote:
> --------------------------------------------------
> -----
> > Firstly, I consider referring to the Seked 5½ as
> > the 4/pi ratio highly misleading.
>
>
> MJ:
>
> You started this thread with the following....
> "...It occurs to me that if I wanted to convey
> through geometry that I knew pi (be it as the
> irrational number 3.1415926xxx or the
> approximation 22/7),
>
> "pi" is set...you are stuck with it...no issue.

Hello Clive,

Farther on in my opening post I wrote, ‘…(again leaving aside whether it is the irrational number 3.1415926... or the approximation 22/7)’.
I was trying to make the point that, for example, the hypothesis that “the length of the KC side wall is to the perimeter of the wall as the diameter of a circle is to its circumference” is regardless of whether one takes the diameter-to-circumference ratio to be the irrational number 3.1415926... or the approximation 22/7.

As I see it, the problem here is that I (and others?) see pi as an irrational number and pi as the approximation 3 1/7 or 22/7 as two distinctly separate things, whereas you (and others?) appear to be seeing them as one and the same and therefore fully interchangeable.
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I wrote, ‘Seked 5½ is equivalent to our cotangent 1.272727’

You reply, A cotangent is the inverse of a tangent and a tangent is the opposite side of the angle compared to the adjacent side (SOCATOH

Marvellous, isn’t it, for the last thirty odd years I referred to the Seked’s rise/run as tangent xxxx, then, quite recently, I read in Gilling’s book on Egyptian maths: “We may consider the sekeds given in the pyramid problems of the RMP and MMP to be the cotangents of the angle of slope of the faces of pyramids.” – on the strength of which I changed all my references to tangent to cotangent.
It now appears I misinterpreted Gillings… ah, well, I’ll just have to change cotangent back to tangent – thank goodness for “find & replace”.
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You wrote, ‘...the 4/pi is the "tangent".

Not when its 280rc height over 220rc base, it isn’t.
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I wrote, ‘…recurring, which equals 51:50:34; whereas 4/pi is equivalent to our cotangent 1.273239545, which
equals 51:51:14.31.

You ask, ‘What's with all of these decimals suddenly?’

It’s needed to highlight the minor difference between tangent 4/pi and tangent 28/22.
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I wrote, ‘Another point we need to keep in mind here is that the pi ratio is a product of fairly sophisticated mathematics, whereas the 3 1/7 ratio can be found by practical measuring and the simplest arithmetic.’

You reply, ‘The term "pi" was derived by a mathematician 2,600 years ago who "discovered" that the circumference of a circle measures (3 + 1/7th) of its diameter.
Yes, Archimedes of Syracuse (287-212 BC). He obtained the approximation 22/7 (I confess I had to look that up on Google).
You continue, ‘He actually ran about town telling everybody.’

Er, wasn’t that Archimedes running amok in only his bath towel after ‘displacing’ his bathwater?
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You write, ‘Now you are attempting to convince the reading public that it's "a product of fairly sophisticated mathematics". Since when were you the judge?’

I think you are getting things a mite confused here, Clive.
I suggest you take a look at [www-groups.dcs.st-and.ac.uk] which explains the situation far, far, better than I ever could.
It would also help you considerably, I believe, if you were to read up on the Egyptian Mathematical Papyri, with particular attention to the problems concerning the calculation of the area of a circle, etc.
As for me being “the judge” of these things, it’s nothing to do with me, but it does have everything to do with Peet, Gillings, Shute & Robins, Rossi et al.
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I wrote, ‘Secondly, I don’t follow what you mean by, ‘why does it "coincidently" fit into the Rc design?’
(I’m presuming you mean Kc – i.e. King’s Chamber)

You reply, ‘You avoided the first part of my question...answer that then I'll follow.’

Actually, I overlooked it, but never mind.
Okay, so you asked, ‘1) How did the architect "realize" the 14:11 seked (4/pi) ratio’ (just to hammer the point home, I should mention again that the 14:11 seked (actually Seked 5 ½) is not the same thing as the (4/pi) ratio).

I presume you are you asking: How did the architect discover Seked 5½?
Well, Corinna Rossi answers this for me in her book Architecture and Mathematics in Ancient Egypt Cambridge University Press 2003, Page 215-216, Sub-heading: “Seked 5 ½ palms, generally called 14/11 triangle”.
I can’t quote or attempt to paraphrase Rossi right now, so I recommend that you track down the text for yourself.
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I wrote, ‘This highlights the highly important and pertinent fact that there is more than one way of arithmetically or mathematically reproducing the dimensions of the side (north and south) walls of the King’s Chamber, which then begs the question: which of the two methods, if either, was the method used by Khufu’s architect?

You reply, ‘It does not...! It shows that you "assumed" the total perimeter is equal to the pi ratio and I'm being the Devil's advocate by explaining that it is equal to the sum of integers and the sqrt of one of those values.

Hmm, I’m not assuming anything, Clive.
It is a simple matter of fact that the actual perimeters of the KC’s side (north and south) walls when divided by the actual lengths of the walls gives a figure close to the diameter-to-circumference ratio (it is irrelevant here and now whether the ratio is taken to be irrational pi or approximation pi).
It was Flinder’s Petrie who first suggested that this appearance of the ratio could be (or was?) intentional.
Your observation that the dimensions are “…equal to the sum of integers and the sqrt of one of those values.” may well be mathematically sound, but this does not mean that it definitely is what the architect intended.
The same point equally applies to Petrie’s view.
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You wwrite, ‘You tell me that AE mathematical papyrus does not provide proof of the AE understanding pi …’

Rather than just have me telling you “that AE mathematical papyrus does not provide proof of the AE understanding pi”, why don’t you – yes, folks, here we go again – read Peet, Gillings, Shute, Rossi et al?

You continue, ‘…and now you are driving your car from the other side of the road...all within 24 hours of posting.’

Sorry, I don’t know what you mean by this.
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I wrote, ‘Firstly, Clive I am not proposing “the designers used the wall of the Kc to provide us with the pi ratio”.
I am suggesting that the architect utilised the number 3 1/7 in his planning of the side (north and south) walls of the King’s Chamber.
I am most certainly not suggesting that pi is encoded in these side walls.

You reply, ‘MJ...please...!’

Please elaborate.
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Regarding the planning of the KC, I wrote, ‘I suggest that the architect started with a simple 2 x 1 rectangle floor plan (possibly as 2 10x10 squares) and went on from there.’

You write, ‘Then why didn't they use this simple 2:1 arrangement for the Queen's Chamber?’

Well, the most likely answer is: because the architect didn’t want to use the 2:1 arrangement for the floor plan of the Queen’s Chamber.
Perhaps you can tell me why they should have done.
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You write, ‘…It's actually confirming what you are trying to suggest regarding the Kc walls, but you are missing the point once more.’

I can’t see it, Clive.
It would help if you were to tell me what you think I am saying about the planning of the KC’s side (north and south) walls.
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You write, ‘Recalculate all that you know of the Kc and review what I typed...then you will see the connection.’

I have a better idea; you simply tell me what “the connection” is.

MJ