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Re: Ariadne's thread
Posted:
Dec 15, 2011 8:31 AM
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Franz,
Offering distractions such as:
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 "
RMP 31 offers a simple algebra problem
x + (2/3 + 1/2 + 1/7)x = 33
solved by:
(1 + (28 + 21 + 6)/42)x = 33
(97/42)x = 33
x = 33(42/97) = 14 + 2/97 + 26/97
x = 14 '4 '56 '194 '388 '679 '776
using your notation.
You ask what has an Egyptian fraction math problem, filled with unit fraction remainders, have to do with Mayan astronomy that used zero remainders?
The answer is simple. Egyptians wrote out problems in quotients and remainders ... in ways that you do not fairly report. In the case of RMP 31, the quotient was 14, and the remainder 28/97 = 2/97 + 28/97 ... facts that you trivialize over and over again by misreporting the numeration system and the actual math problem.
Mayan astronomy wrote out problems in quotients only. How can any Egyptian lunar year system, that wrote out quotient and remainder data, be directly compared with Mayan astronomy data that only used quotients?
My view: it is important to fairly report a culture's numeration and arithmetic system ... before higher order problems are solved ancient manners.
Best Regards,
Milo Gardner
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