Recent content by Matt Benesi

Thanks berkeman. The x=n=b=c=2 case is probably well known, like Euler's identity, because it's one of those math leverage points associated with pi, and prime number distribution. It's like something one of those math popularizers would mention. People apparently weren't focusing on...

I find myself wondering how many directions an averaged magnetic field is oriented in as I spin a magnet (relative to something else).

I can't use that code, don't have mathematica. I can use the coefficients though. That will help (assuming they are correct). I do like the way I organized them better (in the post a couple up). It makes their growth more apparent (only keeping in the last part of the coefficient, so one...

Coefficients for n=2 case, up to coefficient 5. Once again, any general form would be appreciated. If you recognize the pattern, let me know. At x=2, this reduces to cosine. And yeah, it's something simple you learned in high school. If you ever decide to stop messing with me and...

I'm still plodding through this. Making charts. Since I'm pretty much certain the formulas exist out there somewhere, I'd really like the general coefficient formulas for something I'd like to make in GLSL. Might be a pipe dream, but I think smooth variable strength "cosine" and "sine"...

I was hoping to see you post a working example of Schröder’s equation- I know the wikipedia rehash is... the easiest thing to throw out there, but. Maybe something a bit more like the example I posted for x=1.5: explanations leading up to it, then it in use, results being in line with goals...

That doesn't help- except that I learned I could edit posts and clean up the thread... which is sort of useful. If I get good answers to my questions. Can you explain how to use Schröder's equation? Can you write out an example of its use, since you are familiar with its use, and this is...

I am still stuck on this. I would appreciate some input (wikipedia page, or whatever), as I'd like to use the results. //// post 1 : [/spoiler] Thanks for any help.

That's interesting. If you have GEM, you have a definite agreeable rotation direction measurement direction, unless you're dealing with stuff you can't measure.

Just send them some math, and use intersect language to ask "which way do you rotate?"

That post \uparrow \uparrow \uparrow \uparrow \uparrow is the 12th prime post. :p

I like how PF5 translates to P=16 f=6 5, which is 1665, or 3^2*5 *the 12th prime. I like the 12th prime story... but like it's makers more. :D

3blue1brown rocks. Not sure about dropping the 0 though. Didn't get all the way through. A while back (didn't finish it yet), I started working on a zeta/log chart, with a few switching formulas between them (and I was thinking about using it as a quantization structure for some art). The...

Ohhh. I get what you said earlier now (the cases I mentioned weren't specific enough):

Ok, I'm not following what you're saying. Can you explain it more? I thought in the case of ℝ, that 1^\infty was undefined because for all positive x in ℝ \lim\limits_{n\to\infty} \, x^\frac{1}{n} \, = \, 1. So \lim\limits_{n\to\infty} \, 2^\frac{1}{n} \, = \,\lim\limits_{n\to\infty} \...