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May 2, 2024, 1:45 am UTC    
April 26, 2008 09:14AM
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.
Subject Author Posted

site length = pyramid dimensions?

Jim Alison April 17, 2008 09:03PM

Re: site length = pyramid dimensions?

Clive April 17, 2008 10:09PM

Re: site length = pyramid dimensions?

Jim Alison April 19, 2008 12:12AM

Re: site length = pyramid dimensions?

Clive April 20, 2008 09:14PM

Re: site length = pyramid dimensions?

Kanga April 20, 2008 09:41PM

Re: site length = pyramid dimensions?

Clive April 23, 2008 07:34PM

Re: site length = pyramid dimensions?

Kanga April 23, 2008 07:58PM

Re: site length = pyramid dimensions?

Clive April 23, 2008 09:29PM

Re: site length = pyramid dimensions?

Kanga April 24, 2008 12:36AM

Re: site length = pyramid dimensions?

Clive April 24, 2008 09:34AM

Re: site length = pyramid dimensions?

Jon_B April 24, 2008 11:59AM

Re: site length = pyramid dimensions?

L Cooper April 24, 2008 02:35PM

Re: site length = pyramid dimensions?

Jon_B April 24, 2008 02:59PM

Re: site length = pyramid dimensions?

L Cooper April 24, 2008 04:37PM

Re: site length = pyramid dimensions?

Clive April 24, 2008 04:12PM

Re: site length = pyramid dimensions?

Jon_B April 25, 2008 02:34PM

Re: site length = pyramid dimensions?

Clive April 25, 2008 07:51PM

Re: site length = pyramid dimensions?

Jon_B April 26, 2008 04:40AM

Re: site length = pyramid dimensions?

Clive April 26, 2008 03:30PM

Re: site length = pyramid dimensions?

Jon_B April 27, 2008 04:45AM

Re: site length = pyramid dimensions?

Clive April 28, 2008 05:26PM

Re: site length = pyramid dimensions?

L Cooper April 27, 2008 09:57AM

Re: site length = pyramid dimensions?

Jon_B April 28, 2008 11:55AM

Re: site length = pyramid dimensions?

Clive April 28, 2008 04:45PM

Re: site length = pyramid dimensions?

Kanga April 28, 2008 08:59PM

Re: site length = pyramid dimensions?

Clive April 28, 2008 09:52PM

Re: site length = pyramid dimensions?

Kanga April 29, 2008 12:18AM

Re: site length = pyramid dimensions?

Clive April 29, 2008 01:07PM

Re: site length = pyramid dimensions?

fmetrol April 18, 2008 04:35AM

Re: site length = pyramid dimensions?

Dave L April 18, 2008 05:39AM

Re: site length = pyramid dimensions?

L Cooper April 18, 2008 06:51AM

Re: site length = pyramid dimensions?

Dave L April 18, 2008 07:05AM

Re: site length = pyramid dimensions?

L Cooper April 18, 2008 08:36AM

Re: site length = pyramid dimensions?

Dave L April 18, 2008 10:03AM

Re: site length = pyramid dimensions?

Hermione April 18, 2008 10:16AM

Re: site length = pyramid dimensions?

Dave L April 18, 2008 10:22AM

Re: site length = pyramid dimensions?

L Cooper April 18, 2008 11:38AM

Re: site length = pyramid dimensions?

Dave L April 18, 2008 12:34PM

Re: site length = pyramid dimensions?

Graham Chase April 19, 2008 04:57AM

Clives proposal

Graham Chase April 19, 2008 05:05AM

Re: site length = pyramid dimensions?

Jim Alison April 19, 2008 08:39AM

Re: site length = pyramid dimensions?

Graham Chase April 19, 2008 10:24AM

Re: site length = pyramid dimensions?

Jim Alison April 19, 2008 01:10PM

Re: site length = pyramid dimensions?

Graham Chase April 20, 2008 02:37AM

Re: site length = pyramid dimensions?

Kanga April 19, 2008 10:30AM

Re: site length = pyramid dimensions?

Dave L April 19, 2008 11:24AM

Re: site length = pyramid dimensions?

Graham Chase April 20, 2008 02:55AM

Re: site length = pyramid dimensions?

Graham Chase April 21, 2008 01:28PM

Re: site length = pyramid dimensions?

Dave L April 21, 2008 01:53PM

Re: site length = pyramid dimensions?

Graham Chase April 21, 2008 03:32PM

Re: site length = pyramid dimensions?

Dave L April 21, 2008 04:13PM

Re: site length = pyramid dimensions?

Jim Alison April 21, 2008 07:02PM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 01:54AM

Re: site length = pyramid dimensions?

Jim Alison April 22, 2008 08:03AM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 08:56AM

Re: site length = pyramid dimensions?

Dave L April 22, 2008 04:35AM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 05:28AM

Re: site length = pyramid dimensions?

Dave L April 22, 2008 07:04AM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 07:51AM

Re: site length = pyramid dimensions?

Dave L April 22, 2008 08:51AM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 09:16AM

Re: site length = pyramid dimensions?

Dave L April 22, 2008 10:04AM

Re: site length = pyramid dimensions?

Sirfiroth April 19, 2008 10:17PM

Re: site length = pyramid dimensions?

fmetrol April 20, 2008 12:09AM

Re: site length = pyramid dimensions?

Kanga April 20, 2008 01:07AM

Correction

Kanga April 20, 2008 03:40AM

Re: site length = pyramid dimensions?

MJ Thomas April 20, 2008 01:55AM

Re: site length = pyramid dimensions?

Kanga April 20, 2008 04:00AM

Re: site length = pyramid dimensions?

L Cooper April 20, 2008 09:04AM

Re: site length = pyramid dimensions?

Kanga April 20, 2008 06:40PM

Re: site length = pyramid dimensions?

L Cooper April 21, 2008 06:51AM

Re: site length = pyramid dimensions?

Kanga April 21, 2008 08:03AM

Re: site length = pyramid dimensions?

John Legon April 21, 2008 09:41AM

Re: site length = pyramid dimensions?

L Cooper April 22, 2008 06:08AM

Re: site length = pyramid dimensions?

Jim Alison April 22, 2008 07:46AM

Re: site length = pyramid dimensions?

Graham Chase April 22, 2008 08:04AM

Re: site length = pyramid dimensions?

John Legon April 22, 2008 10:34AM

Re: site length = pyramid dimensions?

MJ Thomas April 20, 2008 04:58PM

Re: site length = pyramid dimensions?

Kanga April 20, 2008 07:00PM

Re: site length = pyramid dimensions?

MJ Thomas April 22, 2008 01:06AM

Re: site length = pyramid dimensions?

Kanga April 22, 2008 01:48AM

Re: site length = pyramid dimensions?

Dave L April 20, 2008 05:13AM

Re: site length = pyramid dimensions?

L Cooper April 20, 2008 11:17AM

Re: site length = pyramid dimensions?

fmetrol April 20, 2008 02:17PM

Re: site length = pyramid dimensions?

Sirfiroth April 21, 2008 12:10AM

Re: site length = pyramid dimensions?

fmetrol April 21, 2008 02:34AM

Re: site length = pyramid dimensions?

lobo-hotei April 20, 2008 04:38PM

Re: site length = pyramid dimensions?

MJ Thomas April 20, 2008 05:10PM

Re: site length = pyramid dimensions?

C Wayne Taylor April 20, 2008 05:47AM

Re: site length = pyramid dimensions?

C Wayne Taylor April 22, 2008 05:53AM

Re: site length = pyramid dimensions?

C Wayne Taylor April 22, 2008 07:05AM

Request

Hermione April 22, 2008 07:10AM

Re: site length = pyramid dimensions?

C Wayne Taylor April 22, 2008 07:41AM

Re: site length = pyramid dimensions?

C Wayne Taylor April 22, 2008 08:20AM

Re: site length = pyramid dimensions?

C Wayne Taylor April 21, 2008 08:32AM

Re: site length = pyramid dimensions?

poundr17 April 23, 2008 08:45AM

Re: site length = pyramid dimensions?

Jim Alison April 22, 2008 10:51PM

Re: site length = pyramid dimensions?

Kanga April 23, 2008 12:25AM

Re: site length = pyramid dimensions?

fmetrol April 23, 2008 03:56AM

Re: site length = pyramid dimensions?

Jim Alison April 23, 2008 08:09AM

Re: site length = pyramid dimensions?

John Legon April 23, 2008 04:10AM

Re: site length = pyramid dimensions?

Jim Alison April 23, 2008 08:18AM

Re: site length = pyramid dimensions?

L Cooper April 23, 2008 01:23PM

Re: site length = pyramid dimensions?

Clive April 24, 2008 04:15PM

Re: site length = pyramid dimensions?

L Cooper April 25, 2008 07:30AM

Re: site length = pyramid dimensions?

Warwick L Nixon April 25, 2008 10:06AM

Re: site length = pyramid dimensions?

MJ Thomas April 25, 2008 02:24PM

Re: site length = pyramid dimensions?

Clive April 25, 2008 01:19PM

Re: site length = pyramid dimensions?

MJ Thomas April 25, 2008 03:50PM

Re: site length = pyramid dimensions?

stargazer April 25, 2008 06:59PM

Re: site length = pyramid dimensions?

MJ Thomas April 25, 2008 07:40PM

Re: site length = pyramid dimensions?

fmetrol April 25, 2008 09:25PM

Re: site length = pyramid dimensions?

Jim Alison April 26, 2008 01:33AM

Re: site length = pyramid dimensions?

stargazer April 26, 2008 08:40AM

Re: site length = pyramid dimensions?

Clive April 26, 2008 06:50AM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 07:40AM

Re: site length = pyramid dimensions?

Clive April 26, 2008 12:04PM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 12:34PM

Re: site length = pyramid dimensions?

Clive April 26, 2008 01:40PM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 01:46PM

Re: site length = pyramid dimensions?

Clive April 26, 2008 10:01PM

Re: site length = pyramid dimensions?

fmetrol April 27, 2008 03:59AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 09:49AM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 10:19AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 10:52AM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 11:45AM

Re: site length = pyramid dimensions?

Chris Tedder April 26, 2008 10:55AM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 12:01PM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 12:30PM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 12:36PM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 12:41PM

Re: site length = pyramid dimensions?

fmetrol April 26, 2008 12:57PM

Re: site length = pyramid dimensions?

stargazer April 26, 2008 01:23AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 09:14AM

Re: site length = pyramid dimensions?

stargazer April 26, 2008 09:28AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 10:17AM

Re: site length = pyramid dimensions?

stargazer April 26, 2008 10:37AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 11:08AM

Re: site length = pyramid dimensions?

stargazer April 26, 2008 07:36PM

Re: site length = pyramid dimensions?

Clive April 26, 2008 06:34AM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 10:03AM

Re: site length = pyramid dimensions?

Clive April 26, 2008 01:50PM

Re: site length = pyramid dimensions?

Hermione April 26, 2008 01:59PM

Re: site length = pyramid dimensions?

Clive April 26, 2008 10:07PM

Re: site length = pyramid dimensions?

Hermione April 27, 2008 08:26AM

Re: site length = pyramid dimensions?

Jon_B April 27, 2008 10:03AM

Re: site length = pyramid dimensions?

Clive April 28, 2008 06:24PM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 05:24PM

Re: site length = pyramid dimensions?

Clive April 26, 2008 09:56PM

Re: site length = pyramid dimensions?

MJ Thomas April 27, 2008 07:09AM

Re: site length = pyramid dimensions?

Clive April 25, 2008 08:46PM

Re: site length = pyramid dimensions?

MJ Thomas April 26, 2008 09:29AM

Three questions

Warwick L Nixon April 26, 2008 11:08AM

Re: Three questions

Clive April 26, 2008 02:07PM

Re: Three questions

Warwick L Nixon April 28, 2008 11:25AM



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