Mike Williamson
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 Dec 4 comment What is the integral of 1/x? Well, calling Ln(-1) = i*Pi is already expanding the standard definition of Ln. In the context described (where A & -A are both real, and the log used is standard), Ln(-1) is undefined. But I'd say the intelligent thing is to break it into two undefined improper integrals with one of the limits at 0 (where it is unbounded). At that point, they can be seen as fully symmetric. Recognizing this symmetry, you can "safely" say the answer is 0. Nov 21 asked Aside from Matrix Multiplication, when else is multiplication not commutative? Sep 24 awarded Autobiographer Jan 15 awarded Critic Jan 15 comment Splitting a sandwich and not feeling deceived Not sure why this choice is getting so many up-votes. It is not envy-free, and it does not particularly ensure an even split. In fact, the author himself says that the first person believes he has AT LEAST 1/nth of the sandwich. This implicitly guarantees that the remaining folks have AT MOST 1/nth of the sandwich. The likelihood, especially after doing this twice over, of everyone getting 1/nth is low. In fact, I can imagine my kids complaining that this just ensures the kid with the quickest / loudest mouth gets the largest piece. Nov 18 comment Suggestions for complicated math concepts that a child can understand @littleO Thanks! I will check out some local groups. We're in the Bay Area, so there are plenty, I'm sure. Even at his school. But now I'm thinking maybe I just set something like this up with him & his friends. Nov 18 comment Suggestions for complicated math concepts that a child can understand Thanks! We already have Zometool. I'm happy getting & using toys with him, but he actually wants something a bit more in the realm of "solving": puzzles, and puzzle-like things, etc. So I'm looking for ways to encourage creative problem solving. Nov 16 asked Suggestions for complicated math concepts that a child can understand Dec 6 comment “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions? Thanks for the "double edit"! The comment regarding the solution for a drum and the connection between ALL complex exponentials and circles is great! I guess my problem was that I was intuitively seeing what you wrote elegantly & explicitly, but not recognizing that the real "magic" is in recognizing that complex exponentials are "magically circular". That's easier for me to get my head around, since it is simply the easiest / simplest way to write a circle as a function: i^x is itself circular, where x is any real number. Thanks so much!! Dec 6 awarded Scholar Dec 6 accepted “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions? Dec 4 comment “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions? Thanks to whomever made all of the equations look prettier! Now I know how to add equations properly in this forum. Dec 4 comment “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions? Hi, yes, I think you are correct. But my question was more fundamental as to WHY this is the case? No definitions of e that I have run across ever use trigonometry to define the number. So how does it "magically" also have this incredibly useful trigonometric property? Doesn't that seem downright crazy to anyone else? Dec 4 awarded Student Dec 4 awarded Supporter Dec 4 asked “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions?