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 Dec20 awarded Caucus Sep30 awarded Explainer Jul25 awarded Notable Question Oct27 comment What is the simplest proof of the pythagorean theorem you know? I would consider this to be more of a demonstration than a proof. Such demonstrations would be undermined if the student has seen disappearing square puzzles. Oct27 revised What is the simplest proof of the pythagorean theorem you know? added 381 characters in body Oct27 answered What is the simplest proof of the pythagorean theorem you know? Sep8 comment why have we chosen our number system to be decimal (base 10) @Marc - Have you got a link to a longer discussion of this? Both the use of $\log(b)$ instead of $b$ and the final result of all radices being equal seem reasonable, but it would be nice to see more on it. Aug8 awarded Yearling Aug8 awarded Yearling Jun8 awarded Caucus May18 awarded Popular Question Apr24 awarded Scholar Apr24 awarded Nice Question Feb25 comment Number of integer solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{1000}$ @Amol: Your question was not tagged diophantine-equations and your English is not perfect (not that I hold that against you), so it was not completely obvious. Maybe you meant Gaussian integers... Anyway, click on the question mark in my first comment. Feb25 comment Fractional differential equation @Emmad: See Fractional Calculus Feb25 comment Number of integer solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{1000}$ I guess you mean solutions for integer $x$ and $y$? Feb25 comment Why is $\sqrt{-2} \sqrt{-3} \neq \sqrt{6}$? @dato: I don't think anyone misunderstood your answer, but rather thought that it did not add anything to the discussion. You presented a simple calculation with no attempt at addressing the underlying issue of multivaluedness and branch-cut conventions. You also didn't address the 2nd part of the question (cf the $1=-1$ that Alex provided). Finally, upvoting to balance a downvote is not a good reason to vote. I don't think your answer was worth a downvote, but I also won't upvote it. Feb25 comment Why is $\sqrt{-2} \sqrt{-3} \neq \sqrt{6}$? @dato: My previous comment was just a poor attempt at humour - not addressed to anyone in particular. "Can you computer do complex analysis?" is a bit of a classic paper that discusses these things in the context of computer algebra. It also discusses the useful "unwinding number" approach to thinking about such problems. Feb25 comment Why is $\sqrt{-2} \sqrt{-3} \neq \sqrt{6}$? Can your human do complex analysis? Feb20 comment Is it A Good Idea To Write Papers With Mathematica? ... Although I've used Mathematica for large, formatted personal notes and research documentation, I don't think I would use it for publishing a document that is meant to be printed. The way you want to read things on a electronic device is not the same way you want things to be printed. Mathematica still is not ideal at the latter. Though a CDF-style interactive document might be the way things go if we are ever to transition into the long touted paperless office.