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Re: Paper on: The Geometric Grids of The Hieratic Numeral Signs
Posted:
Nov 26, 2012 9:01 AM
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Grids do not parse Egypt's numeration systems. the Old Kingdom's binary infinite series, or the Middle Kingdom's finite system shared with classical Greeks, Hellenes and Arabs until 800 AD.
To directly parse square root and its numeration system from any culture, math facts must be understood in
precise details, decoded from ancient texts.
Middle Kingdom Egyptians and Greeks scaled rational numbers by finding an LCM m such that
n/p x m/m = mn/mp
The best divisors of mp were selected that best summed to numerator mp.
Egyptians stressed 1/p and 2/p conversions to teach students to convert n/p to concise unit fractions,
series. There are 10 or more ancient texts that describe this system.
Available Greek era texts offer n/p tables thereby included 1/p, 2/p ... (n-1)/p conversions. For example,
an implici Hibeh Papytrust n/45 table written in 300 BC may be of interest .. TRIVIAL LCM 1, 2 AND 4.
MAKE THE NUMERATIONS SIDE OF THE TEXT
http://planetmath.org/encyclopedia/HibehPapyrus.html
square root was reported by Gillings and R,C, Archibald in a 200 BCE text (page 217 .. MATH IN THE TIME OF THE PHARAOHS ...
SQUARE ROOT OF 164 = 12 + 2/3 + 1/15 + 1/26 + 1/32
without citing the historical method.
The method following Occam's razor says
164^1/2 is nearly (12 + 4/5)2 =
144 + 48/5 + 48/5 + 16/25 = 163 + 21/25
the scribe then converted to unit fraction series by
(4/5 - 2/3) = (2 /15 - 1/15) = 1/15
(1/15 - 1/26) = (21/410)
or, more likely a miss reading of 1/26 is better read as 1/24
(1/15 - 1/24) = 1/40 as Archibald suggests
The scribe then replaced 1/40 with 1/32 since 163 21/25 was not near enough to his professional standard.
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