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Topic: Egyptian fraction math only used quotient and remainder statements
Replies: 18   Last Post: Aug 31, 2012 9:23 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Egyptian fraction math only used quotient and remainder statements
Posted: Dec 15, 2011 11:53 AM

Franz, and list members:

Franz offers a distraction quoted by:

"I don't know what problem number 31 of the Rhind Mathematical Papyrus has to do with Mayan astronomy, but if I must I can also shed light on this problem. In my opinion, the Rhind Mathematical Papyrus offers problems that can be solved on several level. On the first level, beginners learn how to handle unit fraction series. On the advanced level they are asked to solve more demanding problems, and on the highest level they are being told about theoretical insights. RMP 31 on the advanced level is about a geometrical problem, it offers a fine example of Egyptian wit, plus a theoretical insight:

RMP 31 - a granary on a ring

33 divided by 1 "3 '2 '7 equals 14 '4 '56 '194 '388 '679
'776 "

Since 1879 it has been clear that

RMP 31 offered a simple algebra problem

x + (2/3 + 1/2 + 1/7)x = 33

solved by:

(1 + (28 + 21 + 6)/42)x = 33

x = 14 + 28/97

It has been clear since 2006 that 20th century scholars, Gillings, Peet, et al, failed to solve the algebra problem by following Ahmes' shorthand conversion hints:

28/97 solved by considering: 2/97 + 28/97

with 2/97 solved in the RMP 2/n table manner that scaled 2/97 by 56/56 and 26/97 by 4/4, scribal steps that Franz totally ignore by jumping from a false granary problem to a correct quotient and remainder answer.

Please transliterate each of Ahmes' problems as scholars have been doing since 1879. Franz's granary ring is silly.

Please, everyone correct scholarly 20th century translation errors that followed false additive patterns ... that Franz and others oddly 'advocate' thereby 'throwing out the scribal solutions to 2/97 and 26/97 ...

Additional proof is provided by RMP 36, an actual hekat (granary) problem that solved a hekat unity

http://planetmath.org/encyclopedia/RMP36AndThe2nTable.html

such that:

(53/53) hekat solved :

2/53 + 3/53 + 5/15 + 15/53 + 28/53

with

2/53 scaled by 30/30

3/53 scaled by 20/20

5/53 scaled by 12/12

15/53 scaled by 4/4

28/53 scaled by 2/2

with non-additive red auxiliary numbers required to complete each set of remainders recorded as exact unit fraction series.

Best Regards,

Milo Gardner

Date Subject Author
12/15/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/17/11 Milo Gardner
12/17/11 Milo Gardner
12/18/11 Milo Gardner
12/19/11 Milo Gardner
12/20/11 Milo Gardner
12/21/11 Milo Gardner
12/22/11 Milo Gardner
12/23/11 Milo Gardner
1/3/12 Milo Gardner
1/3/12 Milo Gardner
1/6/12 Milo Gardner
1/9/12 Milo Gardner
1/19/12 Milo Gardner
2/10/12 Milo Gardner
8/31/12 Milo Gardner