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Plato's mathematics
Posted:
Sep 21, 2008 12:43 PM


David Fowler's esteemed book on this topic is reviewed on:
http://www.maa.org/reviews/mpa.html
Note the supposition that common fractions (vulgar fractions) may have been unknown to Greeks, and therefore Egyptians.
However, Fibonacci 1,600 years later, writing in the Liber Abaci, used common vulgar fractions to write his Egyptian fraction 'part' arithmetic by using three notations. Of several issues, which of Fibonacci's three arithmetic notations were only of Greek origin?
That is, Fowler may have 'quickly' jumped to Greek geometry, which he claimed was not arithmetized, while mentioning that Greek arithmetic had been builton magnitudes (without detailing the specifics of Egyptian, Greek or medieval magnitudes).
At this point, it is important to ponder Plato's theoretical ideas that Plato, himself, defined Greek magnitudes. Was Plato's magnitude the same theortical idea, or very similar to the one, that Ahmes had used in 1650 BCE to write his 2/n table, by only using 14 LCM's? Or, was Plato's idea of magnitude the same theoretical, or very near to, the idea that Fibonacci used to begin the first 1/4th of the Liber Abaci's 500 pages (Sigler's 2002 translation)?
Discussing Greek magnitudes as related, in some way, to one, or both, the older Egyptian arithmetic, and/or the later medieval arithmetic, may add meat to the bones of Plato's arithmetic skeleton.
Anyone want to begin the discussion by listing Plato's mathematics, and the structure of the arithmetic used therein?
Please, delay a full discussion of the geometric side of Plato's mathematics until the 'parallel' arithmetic building blocks have been fairly outlined. Best Regards,
Milo Gardner



