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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 7, 2007 6:15 PM
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Franz,

Your translation of RMP 33 looks more like a transliteration, a method used by linguists, rather than a math problem, written by mathematicians. To a mathematician Egyptian algebra involves working Ahmes' algebra problems and translating Ahmes' work into modern arithmetic, adding nothing, leaving nothing out.

Ahmes' arithmetic is shown on Wikipedia, per:

http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

with the pertinent section copied per:

"The RMP's 84 problems begin with six division-by-10 problems, the central subject of the Reisner Papyrus. There are 15 problems dealing with addition, and 18 algebra problems. There are 15 algebra problems of the same type. They ask the reader to find x and a fraction of x such that the sum of x and its fraction equals a given integer. Problem #24 is the easiest, and asks the reader to solve this equation, x + 1/7x = 19. Ahmes, the author of the RMP, worked the problem this way:

(8/7)x = 19, or x = 133/8 = 16 + 5/8, "

RMP 33 was and is processed in the same manner, or

(97/42)x = 33

x = 1386/87 = 14 28/97

Ahmes broke 28/97 into two parts, 2/97 and 26/97 and used the RMP 2/n table series for 2/97,

found by the Hultsch-Bruins method

2/97 - 1/56 = (112 - 97)/(56*97) = (8 + 7)/(56*97), or

2/97 = 1/56 + 1/679 + 1/776

(pretty neat, right?)

with Ahmes converting 26/97 by an extension of the Hultsch-Bruins method, as noted by:

26/97 - 1/4 = (104 - 97)(4*97) = (4 + 2 + 1)/(4*97), or

26/96 = 1/4 + 1/97 + 1/194 + 1/388

such that:

28/97 = 1/4 + 1/56 + 1/97 + 1/194 + 1/388 + 1/679 + 1/776

Is Ahmes' logic and answer clear? Note that I have not worked any of Ahmes' intermediate algebra steps in unit fractions, as you have done. Modern arithmetic translations do not require unit fraction aspects to be written out, since beginning vulgar fraction conversions are the key arithmetic facts.

Best Regards,

Milo


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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