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RMP 2/n table and the EMR, each text confirms the other text
Posted:
Apr 23, 2009 12:10 PM


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/ahmespapyrusnewandold.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 nonoptimized 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 outoforder 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



