stargazer Wrote:
-------------------------------------------------------
> “…MMP 10 establishes that the ancient Egyptians
> knew that the circumference of a semicircle was Pi
> x d, and therefore knew that the circumference of
> a circle was C = Pi x d. This would represent a
> considerable mathematical sophistication for these
> times and, if true, would antedate the Greek
> Dinostratus by more than 1,400 years.” Gillings,
> p197-8
>
> “This is indeed the modern formula for the curved
> surface of a hemisphere.
If this interpretation of
> MMP 10 is the correct one, then the scribe who
> derived the formula anticipated Archimedes by
> 1,500 years!" Gillings, p199-200
Emphasis added by me. MJ
Hello Stargazer,
The quote you give is accurate; unfortunately it is out of context.
Taking Gillings entire commentary on this issue clearly shows that there are strong elements of doubt about his interpretation of MMP10 - and some of these doubts are his own!
Concerning MMP10, Gilling's writes (On page 247 of his book - 1982 Dover paperback edition):
"No. 10 deals,
I consider, with the area of the surface of a hemisphere, as Struve thought,
and if this is so, it becomes the outstanding Egyptian achievement in the field of mathematics." (emphases added by me. MJ)
According to Rossi, "Our main sources for defining the ancient Egyptian mathematical system are a number of mathematical texts written on papyri, ostraca and leather dating from the second half of the Middle Kingdom to the Second Intermediate Period (c. 1800 to 1600 BC), the most important of which are the Rhind Mathematical Papyrus (usually abbreviated as RMP), the Moscow Mathematical Papyrus, the Kahun Papyri and the Egyptian Mathematical Roll.
(
Architecture and Mathematics in Ancient Egypt. Corrina Rossi. Cambridge 2007 paperback, page 57).
Regarding the area of a circle in Ancient Egypt, on page 67 of her book, Rossi writes: “… does it really make sense to talk about the approximation of a concept or a number that did not exist in the Egyptian mind? The method used by the Egyptians (take 1/9 from the diameter and square the rest) had nothing to do with the ratio between circumference and diameter, now expressed by pi.”
There is, for me, a rather splendid irony in this – and one I could well do without, to be honest.
My hypothesis on how Khufu’s pyramid and its interior could have been planned would benefit greatly from there being irrefutable proof (ideally contemporary texts) that the Egyptians of the 4th Dyn. knew of and used the ratio between circumference and diameter as 3 1/7 or 22/7.
Sadly, no such evidence exists and I am left to argue that forty-plus clear occurrences (in a, to me, clear pattern) of Dimension A = Dimension B multiplied by 3 1/7 or Dimension A = Dimension B divided by 3 1/7 is evidence of intent and demonstrates that the Egyptians of the 4th Dyn. did indeed know of and use in their planning of their architecture the ratio between circumference and diameter as 3 1/7 or 22/7.
Regards,
MJ
p.s. I think it is worth considering the difference in approach between Gillings and Rossi.
I suggest this difference is down to Gillings being a mathematician and Rossi being an Egyptologist.