tag:blogger.com,1999:blog-264226589944705290.post6777440775738455457..comments2021-12-14T05:53:12.175-08:00Comments on God Plays Dice: The square root of 3 and mock theta functions. (No, they're not connected.)Michael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-264226589944705290.post-21597192838702410022009-01-23T08:29:00.000-08:002009-01-23T08:29:00.000-08:00I replied that I don't think that interpretation h...I replied that I don't think that interpretation holds up in conjunction with Rouse Ball's remark that "It would seem...that [Archimedes] had some (at present unknown) method of extracting the square root of numbers approximately."<BR/><BR/>I'm sitting in Van Pelt right now, and if I gather enough motivation before lunch time I'll see if I can hunt up the original sources. Having the library catalog on my lap doesn't hurt the chances.Mark Dominushttps://www.blogger.com/profile/17698641253266210249noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-56687391038538398612009-01-22T07:02:00.000-08:002009-01-22T07:02:00.000-08:00I wrote the following in an email to Mark this mor...I wrote the following in an email to Mark this morning:<BR/><BR/>I have a slightly different reading of Rouse Ball and Heath's puzzlement. I don't read them as asking, "how could he possibly have done this?" but instead, "how did he actually do this?" They're aware of methods of extracting roots, and even aware of ones that Archimedes could plausibly have used. But a more interesting question to an historian is what he *actually* did.<BR/><BR/>Different methods show hints of different theories, and while the theories might not be worked out in gory detail, they show different patterns of thought about the same problem. Compare the dozens of proofs of the Pythagorean theorem and you'll see a number of different ways of thinking about the situation. Which one a particular author uses tells you something about how he thinks about not only this problem, but mathematics in more generality.<BR/><BR/>Ancient Greek mathematics was usually very geometrical in spirit. The question I'd be interested in is, "did Archimedes have a geometric approximation in mind when deriving these estimates, and if so, which one?"Anonymousnoreply@blogger.com