The Babylonian method for computing square roots is described (among other places) in this Wikipedia article. What evidence is there that they actually used this method?

I have found several references that imply that they did not use an iterative process, but used a closely related method that stopped after a single iteration (see, for instance, Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context, and the Wikipedia notes for Square Root of 2, Note 1).

Yet other references imply that they indeed used the iterative process. In his A History of Mathematics, C. Boyer happily explains the iterative process (which I find unusual because every other sentence in C. Boyer's works usually reads something like, "...but it would be foolish to assume that these ancient mathematicians had any idea what they were doing..."...but I digress).

Going back to the Yale tablet YBC 7289, the Babylonians evidently knew $\sqrt{2}$ to six decimal places. Is it safe to assume they did have an iterative process, based on this and other circumstantial evidence?

  • 2
    $\begingroup$ Your Fowler-Robson reference pretty much answers your question on p. 376:"Both of these alternatives remain conjectural, however, as there is still no direct evidence — by which we mean explicit instructions in the course of a mathematical solution — for the use of more than the first step of the procedure". There is no need to assume they were aware of "iterative process". Someone made a first estimate using the procedure once, a century later someone else applied the same procedure to the first estimate and got a more precise value, which was then put into tables. $\endgroup$ – Conifold Apr 21 '18 at 6:19
  • $\begingroup$ Roger that. I was curious if I had missed any other important references. The Fowler-Robson paper seems to be the most legit analysis I've found (and one that other sites/papers reference) so I'll stick with that. $\endgroup$ – Brant Apr 22 '18 at 21:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.