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I'm interested in learning more about the Bloom of Thymaridas, a description of which can be found here.

Obviously the mathematics behind the identity is not particularly deep from a modern standpoint. However, does anyone have any information on why it was considered a notable arithmetical method during its time? Were there some common scenarios in which you would be given those particular sums and needed to solve for x?

Thanks!

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    [An apropos (and rather interesting) paper.](http://logica.ugent.be/albrecht/thesis/Reception.pdf) My understanding of [Heath](http://books.google.com/books?hl=en&id=drnY3Vjix3kC&pg=PA94), however, is that Iamblichus did not mention in his writings what made Thymaridas consider his *epanthema*.2012-01-10
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    Just a guess, based on the culture that produced Iamblichus and the works he commented on (I have no specific historical knowledge): it is unlikely that there were any "common scenarios," outside of purely invented mathematical or even numerological ones, in which one would have met this problem. Generally, Pythagorean number theory wasn't about "common scenarios." (So-called "perfect" numbers are a good illustration of this: by any standard that would have been relevant to non-Pythagoreans in antiquity, there is no "context" in which they arise. It's just the pure study of numbers.)2012-01-10
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    ... (continuing my comment) as for why it was later considered notable, my guess is that medieval scholars were simply enormously pleased to have any mathematics at all from antiquity. Europe had gone through centuries in which (roughly) no mathematics was done at all, and to find things like this must have astonished them. (The general practice of solving systems of equations is of course enormously useful. But I do not think later scholars put ancient results on specific problems like this to any particular "use".) Again, this is just my personal speculation.2012-01-10

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