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Re: Undergraduate Publication to Math History Journals?
Posted:
Apr 21, 2012 12:45 PM
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David,
A short paper adds facts to your Euclid point of view:
http://mpiwg-berlin-mpg.academia.edu/SonjaBrentjes/Papers/1541517/On_some_theorems_to_elementary_number_theory_by_kamal_al-din_farisi
May a required numeration question be mentioned? The above author makes no claim of parsing Euclid data from historical Egyptian fraction weights and measures or other numeration limitations that dominated Greece and Persia in different ways over 2,000 years.
One way to link medieval number theory with Greek parents and Persian/modern children follows Fibonacci's 1202 AD LIBER ABACI, Latin speaking/writing Europe's arithmetic book for 250 years.
An English translation was published in 2002 ... authored by L.E. Sigler ... a 500 page book that takes 125 pages to disclose seven rules (distinctions) that generally converted rational number n/p to concise and awkward unit fraction series in a subtraction context:
(n/p - m) = (mn - p)/mp
with (mn -p) set to unity (1) as often as possible.
Parameter m was a least common multiple m that Greeks and Egyptians used in a closely related multiplication context that scaled n/p by (m/m) such that
n/p (m/m) = mn/mp,
with the best divisors of mp selected that summed to mn, thereby calculating a concise unit fraction series used for theoretical and applied purposes.
The 300 AD Hibeh Papyrus
http://planetmath.org/encyclopedia/HibehPapyrus.html
offers several historical lessons.
Of oourse, Euclid's geometric numbers skips over important aspects of the intellectual war that took place when Egyptian fraction numeration ended in 1454 ad --- when the Ottoman Empire over ran the Byzantine Empire ... closing the Silk Road ... and much more ... with replacement base 10 decimals born in 1585 AD ...
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