MJ Thomas Wrote:
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> Hello Hermione,
>
> I wrote, 'That the perimeter of a square is always
> 4 times the length of a side is not mentioned
> (AFAIAA) in any of the Mathematical Papyri, so are
> we then to assume that the AEs did not know:
> Perimeter of a square = 4 times length of a
> side?'
>
> You reply, 'That is a simple, self-evident
> mathematical fact.'
>
> If a square measures 4.743 units, then what is its
> perimeter?
> Now, you can either physically do a continuous
> measure of the perimeter or you can calculate it
> as P = length of side @ 4.743 units time 4.
> The thing here about the irrational number pi is
> that strictly speaking it cannot be physically
> measured.
> However, what can be done and is still done to
> this day - and this despite our clever, highly
> advanced technology and mathematics - is to take
> the circumference of a circle to be approximately
> 3 1/7 times the diameter of that circle.
> How was this simple approximation arrived at?
> Various people in various parts of the world drew
> a circle (usually, I imagine, with a couple of
> pegs and a piece of cord, string, or whatever) and
> then did a continuous measure of the circumference
> - eventually various people in various parts of
> the world twigged that the circumference of a
> circle is always approximately 3 1/7 times the
> diameter.
> Given that their royal cubit was divided into 7
> palms, I expect that the AEs were amongst the
> first to do said twigging...
One thing that could have been done was to invent two different units: one that measured 3 1/7 times the other (rather like the remen and the RC). One set of units - y - could have formed the diameter; and the same number of units - y - could have been used with the larger units to set out the circumference.
However, I don't know of any evidence to this effect.
> You write, 'A knowledge of pi is, OTOH, more
> complex. So I therefore don't see how your
> argument could be used to imply that the AE
> realized the significance of the ratio 22/7.'
>
> Well, the point is that pi and 3 1/7 are quite
> simply not, repeat not, the same thing.
I am aware of that.
> Pi is significant because it is an irrational
> number, and so on and so forth.
> 3 1/7 is totally insignificant.
> 3 1/7 as the ratio of diameter-to-circumference
> has no more significance than has a square’s
> perimeter being 4 times the length of one of its
> sides.
>
> Saying that multiplication and division by 3 1/7
> (22/7) was used in the planning of the dimensions
> of Khufu’s pyramid and its passages and chambers
> is not saying that the planning of the Pyramid's
> dimensions involved pi.
>
>
> You write, 'Without a sight of all the evidence -
> presumably the material in the 300 pages that
> you've already mentioned - I don't think I could
> comment further on this.'
>
> Fair comment - and you presume correctly.
> Until I am ready to present my hypothesis, I
> strongly recommend that you and others here
> several times each and every day repeat to
> yourself: 3 1/7 is not pi. Pi is not 3 1/7.
... and there is no evidence that pi was used in the architecture of the GP.
Hermione
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