Simon
Reputation
775
Top tag
Next privilege 1,000 Rep.
Create new tags
 Oct 27 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. Sep 8 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. Feb 25 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. Feb 25 comment Fractional differential equation @Emmad: See Fractional Calculus Feb 25 comment Number of integer solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{1000}$ I guess you mean solutions for integer $x$ and $y$? Feb 25 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. Feb 25 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. Feb 25 comment Why is $\sqrt{-2} \sqrt{-3} \neq \sqrt{6}$? Can your human do complex analysis? Feb 20 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. Feb 20 comment Is it A Good Idea To Write Papers With Mathematica? @3Sphere: Cascading stylesheets gives you the formatting and would also take care of formatting macros. Other TeX-like macros are possible, but not so straightforward. Assembling large documents from smaller is definitely possible, manipulating and creating notebooks using the kernel is quite easy. If I was writing a long thesis or a book in Mma I would probably take this route (and I'm sure others have). Feb 19 comment Is it A Good Idea To Write Papers With Mathematica? @3Sphere: Notebooks are plain text files, so can be treated like source code. Turn off FileOutlineCache and TrackCellChangeTimes and it then plays with version control quite nicely. Feb 19 comment Is it A Good Idea To Write Papers With Mathematica? @Ben: I agree that vendor lock-in is a problem, but it isn't so much of a problem now that there is the free CDF player, which can read notebook files. Jan 16 comment Inverse of the polylogarithm @Sasha: You're probably (almost certainly) right about non-integer $n$, but more often than not, the integer case is the one that occurs. In particular, my question asked about the inverse dilog separately from the general polylog. Jan 13 comment Finding General Expression from recursion A hypergeometric function can be defined as a exponential generating function of a hypergeometric series. This does not really correspond to what you have above... Although, maybe you mean something different. (Also, these types of comments aren't really appropriate as answers in this site) Jan 12 comment Optimal Towers of Hanoi strategy (3 pillars, from pillar A directly to C not allowed) @Brian: Oh yeah. I guess that means my brain has stopped working for the night and it's time to go to bed. Sorry about the confusion. Jan 12 comment Optimal Towers of Hanoi strategy (3 pillars, from pillar A directly to C not allowed) What do you mean "It is not allowed to move a disk from pillar A to pillar C directly"? The second move has to be from A to C, at least in the Tower of Hanoi that I know... By the way, this is a classic problem and the linked to wikipedia article has lots of spoilers. I suggest you don't look past the introduction. Jan 12 comment Finding General Expression from recursion Your new edit is a very special choice of $P_1$. It's equivalent to choosing the initial condition $P_{-1} = 0$ (and $P_0$ unfixed)... Jan 12 comment Finding General Expression from recursion @Verbeia: Or just any two $P_i$s... Dec 15 comment What is the analytic form of MeijerG in Mathematica? @Sasha: So maybe reading isn't my strong suit... Dec 15 comment What is the analytic form of MeijerG in Mathematica? The naive, analytic continuation approach to "fractional" calculus is the best! (I use it all the time in dimensional regularization)