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Topic: One Euro-centric BBC report of the British Museum "owned" RMP
Replies: 18   Last Post: Jul 6, 2010 10:50 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Re: One Euro-centric BBC report of the British Museum "owned" RMP
Posted: Jul 5, 2010 8:50 AM

Thank you for the comment. RMP problems must be read considering all scribal details. Truncating RMP 38 data, for example, omitting a discussion of Ahmes' inverse aspect of scribal division and multiplication operations, throws a beautiful baby out with the bath water.

An Ahmes blog:

http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html

reports a vivid RMP 38 context: "In RMP 38 two rational numbers, (35/11)/10 = 35/110 = 7/22, were multiplied 320, by a doubling ' method citing:

1. Initial calculation

(320 ro)*(35/11) = (320 ro)*(2/3 + 1/3 + 1/6 + 1/11 + 1/22 + 1/66)/10 = 101 + 9/11 ro

2. Proof

(101 9/11 ro) was multiplied by 22/7, and returned one hekat , 320 ro.

This class of hekat calculation infers that the traditional Old Kingdom pi value of 256/81 was corrected by considering : " ... that (7/22) and (22/7) were shown and proved to be inverses, and that the AE scribes were skilled and aware of the natural inverse operations of multiplication and division. In effect, the AE were adept at finding reciprocals" (Bruce Friedman)!"

On a deeper level, modern scholars must discuss 320 times 7/22 = 101 9/11, at some point, by showing how and why 9/11 was converted to a unit fraction series. Omitting fundamental arithmetic discussions of Ahmes' proof that 101 + 9/11 was converted to a unit fraction series in the context of a 2/n table method throws a much larger baby out with RMP 38 bath water.

RMP 38 is a wonderful example of scribal arithmetic. Reading RMP 36 in terms of Ahmes' 2/n table method shows that Middle Kingdom scribes scaled n/p by an LCM m to mn/mp. When possible mn/mp was written as a unit fraction series by selecting the divisors of denominator (GCD) mp that summed to numerator mn.

In the 101 + 9/11 case

101 remained as a quotient, and

9/11 was scaled to LCM 6 such that

54/66 selected divisors of 66: 44, 33, 22, 11, 6, 3, 2, 1 that summed to numerator 54 by

(44 + 6 + 3 + 1)/66 = 2/3 + 1/11 + 1/22 + 1/66

(101 + 2/3 + 1/11 + 1/22 + 1/66)ro = (101 + 9/11)ro

To ponder additional Ahmes arithmetic details a Math 2.0 Webinar will focus on Ahmes and Fibonacci's common proto-number theory rational number conversion methods. The one hour open forum discussion will be available for viewing after July 21, 2010 on:

http://mathfuture.wikispaces.com/Egyptian+math

Best Regards,

Milo Gardner

Date Subject Author
2/20/10 Milo Gardner
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