Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: RMP 2/n table and the EMR, each text confirms the other text
Replies: 4   Last Post: May 9, 2010 1:09 PM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Milo Gardner Posts: 1,105 Registered: 12/3/04
RMP 2/n table and the EMR, each text confirms the other text
Posted: Apr 23, 2009 12:10 PM
 Plain Text Reply

Dear Forum members,

To fairly decode/translate the RMP 2/n table, an earlier Egyptian text must be found that used a related method. Scholars in the 20th century muddled Ahmes 'ab initio' 2/n table and EMLR calculations, not recognizing a related pattern. Using the EMLR as a foundation document, as read in 2001, and updated in 2006, Ahmes used a closely related optimized LCM multipliers (b/b), meaning a = a(b/b) = ab/a ( http://en.wikipedia.org/wiki/RMP_2/n_table and http://rmprectotable.blogspot.com/ ).

For example, Ahmes consistently converted 2/97 to an optimized unit fraction series, in the 2/n table and RMP 31 and 33 ( http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html ) by selecting the LCM 56 written as 56/56, or:

2/97(56/56) = 112/5432 = (97 + 8 + 7)/5432 =

1/56 + 1/679 + 1/776

the 250 year older EMLR used non-optimized LCMs in the form of b/b,
(http://en.wikipedia.org/wiki/Egyptian_Mathematical_Leather_Roll) .

For example 1/8 was converted by three different LCMs 3/3, 5/5, and 25/25. The LCM 25/25 case was assisted by 6/6, such that:

1/8*(25/25) = 25/200 = (8 + 17)/200 = 1/25 + 17/200

with,

17/200*(6/6) = 102/1200 = (80 + 16 + 6)

= 1/15 + 1/75 + 1/200

an unusual out-of-order series, recorded on EMLR line 8.0,

1/8 = 1/25 + 1/15 + 1/75 + 1/200

The 1/8 EMLR conversion is confirmed by a second EMLR conversion (1/16 to 1/50 + 1/30 + 1/150 + 1/400).

Comments would be appreciated.

Best Regards,

Milo Gardner

Date Subject Author
4/23/09 Milo Gardner
4/23/09 Milo Gardner
5/9/10 Milo Gardner
4/23/09 Milo Gardner
5/9/10 Milo Gardner

© The Math Forum at NCTM 1994-2018. All Rights Reserved.