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Topic: RMP # 48
Replies: 70   Last Post: Jul 23, 2010 8:57 AM

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Milo Gardner

Posts: 1,105
Registered: 12/3/04
Re: RMP # 48
Posted: Oct 2, 2007 8:54 AM
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Lee,

One of the MMP's most noted problems does not include the idea of slicing a semisphere, as you have interjected. I had not mentioned the point (though others have). The most noted problem in the MMP reports slicing a truncated pyramid into exact pieces. Adding up the pieces finds the area, using Egyptian fractions, no more, no less.

The anti-Black Athena review of MMP 10 stressed a proposed link to Eudoxus and Archimedes without stating the 1/4th geometric (infinite) series Egyptian fraction details,

4A/3 = A + A/4 + A/16 + A/64 + ... + A/4n + ...

which Archimedes converted to a finite Egyptian fraction series,

4A/3 = A + A/4 + A/12

as one slice needed to exactly sum the area, much as the MMP did 1,500 years earlier.

Returning to MMP 10, Peet's views of Egyptian fraction arithmetic have been half-correct, hence misleading in certain respects. Peet threw out the baby out with the bath water when he discussed the correct geometrical cylinder view of the problem. However, read Peet's review of the Akhmim Wooden Tablet, and his slam against the 1906 paper written by Daressy.He did not understand the basis of the Egyptian fractions being used (remainder arithmetic, with Egyptian fractions being scaled to 1/320 hekat remainders), though he did agree that a ro meant 1/320 of a hekat. It took 96 years, until 2002, for the typographical errors introduced by Daressy to be corrected by Vymazalova, a Charles U. graduate student. Peet did the same thing (not grasping the non-additive aspects of Egyptian fraction series) when discussing MMP 10. Peet did not understand the finite basis of Egyptian Egyptian fraction series, since he only saw the additive aspects of the EMLR, RMP and all the Egyptian fraction documents.

Beauty is in the eye of beholder - and Peet saw no non-additive beauty in Egyptian fractions, as Ahmes and the Middle Kingdom scribes saw when they solved the Horus-Eye problem exactly writing

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ...

as an exact Egyptian fraction series,

by using any rational number as an exact remainder, such as, the remainder 1/64 as 5/320 into ro units, per

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (4 + 1)/320

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 4 ro + 1ro.

Best Regards,

Milo Gardner


Date Subject Author
9/30/07
Read RMP # 48
L. Cooper
10/1/07
Read Re: RMP # 48
Franz Gnaedinger
10/1/07
Read Re: RMP # 48
L. Cooper
10/1/07
Read Re: RMP # 48
Milo Gardner
10/1/07
Read Re: RMP # 48
L. Cooper
10/2/07
Read Re: RMP # 48
Milo Gardner
10/3/07
Read Re: RMP # 48
Milo Gardner
10/3/07
Read Re: RMP # 48
L. Cooper
10/3/07
Read Re: RMP # 48
Franz Gnaedinger
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
Milo Gardner
10/4/07
Read Re: RMP # 48
L. Cooper
10/5/07
Read Re: RMP # 48
L. Cooper
10/5/07
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
L. Cooper
10/6/07
Read Re: RMP # 48
Franz Gnaedinger
10/6/07
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
L. Cooper
10/6/07
Read Re: RMP # 48
Franz Gnaedinger
10/6/07
Read Re: RMP # 48
Milo Gardner
10/7/07
Read Re: RMP # 48
Franz Gnaedinger
10/7/07
Read Re: RMP # 48
Milo Gardner
10/7/07
Read Re: RMP # 48
Franz Gnaedinger
10/7/07
Read Re: RMP # 48
Milo Gardner
10/8/07
Read Re: RMP # 48
Franz Gnaedinger
10/8/07
Read Re: RMP # 48
Milo Gardner
10/8/07
Read Re: RMP # 48
Franz Gnaedinger
10/8/07
Read Re: RMP # 48
Milo Gardner
10/9/07
Read Re: RMP # 48
Franz Gnaedinger
10/9/07
Read Re: RMP # 48
L. Cooper
10/10/07
Read Re: RMP # 48
Franz Gnaedinger
10/11/07
Read Re: RMP # 48
Franz Gnaedinger
10/11/07
Read Re: RMP # 48
L. Cooper
10/12/07
Read Re: RMP # 48
Franz Gnaedinger
10/12/07
Read Re: RMP # 48
Franz Gnaedinger
10/12/07
Read Re: RMP # 48
L. Cooper
10/13/07
Read Re: RMP # 48
Franz Gnaedinger
10/13/07
Read Re: RMP # 48
L. Cooper
10/13/07
Read Re: RMP # 48
Franz Gnaedinger
10/15/07
Read Re: RMP # 48
Franz Gnaedinger
10/18/07
Read Discussion of error/mistake in Greek texts
Ed Wall
10/19/07
Read Re: Discussion of error/mistake in Greek texts
Franz Gnaedinger
10/20/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/5/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/14/07
Read Re: Discussion of error/mistake in Greek texts
Franz Gnaedinger
12/14/07
Read Re: Discussion of error/mistake in Greek texts
Milo Gardner
12/14/07
Read Schools of Egyptology, and why they are not leaders in scribal math studies
Milo Gardner
10/11/07
Read Re: RMP # 48
Milo Gardner
10/12/07
Read Re: RMP # 48
L. Cooper
10/12/07
Read Re: RMP # 48
Milo Gardner
10/13/07
Read Re: RMP # 48
L. Cooper
7/11/10
Read Re: RMP # 48
Dioxippus
7/12/10
Read Re: RMP # 48
Milo Gardner
7/20/10
Read Re: RMP # 48
Dioxippus
7/21/10
Read Re: RMP # 48
Milo Gardner
7/21/10
Read Re: RMP # 48
Dioxippus
7/21/10
Read Re: RMP # 48
Milo Gardner
7/23/10
Read Re: RMP # 48
Dioxippus
7/23/10
Read Re: RMP # 48
Milo Gardner
10/6/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/8/07
Read Re: RMP # 48
Milo Gardner
10/11/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/12/07
Read Re: RMP # 48
Milo Gardner
10/13/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/13/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/19/07
Read Re: RMP # 48
Hossam Aboulfotouh
10/27/07
Read Re: RMP # 48
Matt Hugh

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