## Search found 6065 matches

Sat Jul 21, 2012 7:01 am UTC
Forum: Mathematics
Topic: An alternating sum
Replies: 7
Views: 3588

### Re: An alternating sum

Just because a series converges does not mean that there is necessarily a simple, pretty expression that it simplifies to. After a bit of hunting around on Wikipedia, this series may equal d/ds Li s (-1) evaluated at s = 1, where Li s (z) is the polylogarithm function. Whether this is in any way mor...
Wed Jul 18, 2012 9:13 pm UTC
Forum: Science
Topic: LDF as Gravity--Fringe stuff
Replies: 17
Views: 3592

### Re: LDF as Gravity--Fringe stuff

If Newton knew about these forces, then he probably would have known that the attraction of matter would not go down as 1/r^2, but rather 1/r^6. He would have seen that planetary orbits were unstable, and he would throw this explanation out. I'm not entirely sure exactly how this force is affected w...
Wed Jul 18, 2012 9:23 am UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 92257

### Re: "Oh no! We forgot how to say... math... stuff!"

Something that has bugged me for a while is that there are a few conflicting conventions for defining spherical coordinates. In my vector calc class, our convention was: x = r * cos(θ) * sin (φ) y = r * sin (θ) * sin (φ) z = r * cos (φ) or something like that (I may have mixed up φ and θ). You can i...
Sat Apr 21, 2012 6:00 am UTC
Forum: Mathematics
Topic: Split-Octonians and Beyond
Replies: 1
Views: 1296

### Split-Octonians and Beyond

There are a couple of things on my mind. Firstly, I have gotten quite comfortable working with octonions and split-octonions. The latter of these piqued my curiosity when I heard that they can be used to represent polar vectors (or simply vectors) that are common in high school to undergrad-level ph...
Sun Apr 08, 2012 5:27 am UTC
Forum: Mathematics
Topic: Favorite number sequences?
Replies: 24
Views: 4270

### Re: Favorite number sequences?

I am myself quite partial to fractal sequences such as the sequence a(n) that you get when the digits of the nonnegative integer n (in base 2, in this case) are added together: 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5, 2,3,3,4,3,4,4,5,3,4,4,5,...
Sun Mar 04, 2012 4:47 am UTC
Forum: Religious Wars
Topic: Chess vs. Go Which is the better board game.
Replies: 55
Views: 29399

### Re: Chess vs. Go Which is the better board game.

I love both games for different reasons, but the inner geek decrees go to be superior game. There is something extremely appealing about a game that can be taught to a four-year-old, yet which exhibits a degree of complexity beyond belief. It is the ultimate example of "easy to learn, hard to m...
Wed Jan 11, 2012 6:32 am UTC
Topic: 1002: "Game AIs"
Replies: 251
Views: 109345

### Re: 1002: "Game AIs"

Not sure about all of you guys, but my greatest hope is to see the day when a computer program can consistently beat the greatest humans at go (kind of like chess, currently). That is truly the day that AI will have been perfected.
Mon Apr 25, 2011 1:40 pm UTC
Topic: 0889: "Turtles"
Replies: 207
Views: 60083

### Re: 0889: Turtles

Oh, and cyanyoshi, I thought Filler Art was hilarious. You have to know the whole webcomics milieu to really appreciate it, though. Okay, I guess I stand corrected. From this discussion, it is pretty clear that all of xkcd's comics appeal to some portion of fans. Therefore, there is no worst comic....
Sat Apr 23, 2011 3:48 am UTC
Topic: 0889: "Turtles"
Replies: 207
Views: 60083

### Re: 0889: Turtles

aegiswings wrote:ok, enough arguing.

Can we all just agree that this is the worst. xkcd. ever?

If you don't agree, which one is worse?

No, this is not the worst xkcd ever. This one is worse: 404. Also, there's this: Filler Art.
Fri Apr 22, 2011 5:40 pm UTC
Topic: 0889: "Turtles"
Replies: 207
Views: 60083

### Re: 0889: Turtles

Randall was obviously not on drugs when he wrote this (compare to http://xkcd.com/68/ ). I took this comic as a sympathetic parody of stoner culture. This is not his best work ever, but I'll take it.
Wed Feb 16, 2011 5:03 am UTC
Topic: 0861: "Wisdom Teeth"
Replies: 116
Views: 27902

### Re: 0861: "Wisdom Teeth"

No alt-text? What the...

Edit: That's more like it! However, the xkcd app that I have for iTouch refuses to acknowledge that alt-text was added.
Wed Jan 19, 2011 6:38 am UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 9232

### Re: ln(x) or log(x)?

I like to write log(x)/log(b) to avoid ambiguity. I guess I got used to writing it like this to input into scientific calculators. Anyway, I generally mean log(x) to be base e when I talk on the internet, but write a cursive "ln" instead of "log". That's how I roll. Also, I am al...
Wed Jan 19, 2011 6:29 am UTC
Topic: 0849: "Complex Conjugate"
Replies: 96
Views: 24576

### Re: 0849: "Complex Conjugate"

Yes, multiplying something by its complex conjugate results in a real number. In this comic, Randall turns this into a terrible pun and then points out that repeating such a terrible pun will annoy people to the point that they ditch you. Thanks, Einstein. :P Almost makes me want to not let Randall...
Sun Dec 12, 2010 7:30 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 489303

### Re: Favorite math jokes

Why was six afraid of seven?...Because seven "eight" nine!

Why was seven afraid of eight?...Mathematical induction.

Oh. You already heard that one...
Fri Dec 03, 2010 5:24 am UTC
Topic: 0829: "Arsenic-Based Life"
Replies: 100
Views: 20694

### Re: 0829: "Arsenic-Based Life"

Geeky, relevant, and absolutely hilarious. This strip has it all, and WOW at the timing! Great job.
Wed Dec 01, 2010 7:14 am UTC
Topic: 0828: "Positive Attitude"
Replies: 92
Views: 21604

### Re: 0828: "Positive Attitude"

Well, I think we are all grateful that Randall's creative juices are still flowing. A most excellent strip today! Oh, and I just realized that it is December! Double super special awesome!
Wed Dec 01, 2010 6:58 am UTC
Topic: 0204: "America"
Replies: 19
Views: 11010

### Re: 0204: "America"

We must never forget.
Wed Nov 24, 2010 7:17 am UTC
Topic: 0824: "Guest Week: Bill Amend (FoxTrot) "
Replies: 127
Views: 32458

### Re: 0824: "Guest Week: Bill Amend (FoxTrot) "

Wow. The format was brilliant! I found each of the four subcomics rather groan-inducing, but this comic as a whole is charming! Jason would definitely do all of that, which makes me smile!

Yo dawg, I herd you liek comic strips!
Fri Nov 19, 2010 5:13 am UTC
Topic: 0821: "Five-Minute Comics: Part 3"
Replies: 143
Views: 35630

### Re: 0821: "Five-Minute Comics: Part 3"

I love all the quick laughs! I am still giggling about the Jupiter sub-comic. Fastest gun in the west made me laugh out loud. The breastfeeding one is kind of wierd.
Thu Nov 18, 2010 6:42 am UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 13102

### Re: Disguised forms of 2

$2 = \sqrt[3]{10+\sqrt{108}}+\sqrt[3]{10-\sqrt{108}}$
Fri Sep 24, 2010 3:24 pm UTC
Forum: Mathematics
Topic: Doubts about my physics study: am I smart enough?
Replies: 19
Views: 5712

### Re: Doubts about my physics study: am I smart enough?

In the opinion of a first-year engineering student in a US college, the best way to see if you have what it takes to study math, physics, etc. is to try them out for a while. It seems like you have the work ethic required to excel in pretty much anything, so as long as you make a solid attempt to st...
Thu Sep 23, 2010 7:24 pm UTC
Forum: Mathematics
Topic: Convergence Problem
Replies: 13
Views: 2235

### Re: Convergence Problem

Thanks. Those explanations help a lot!
Thu Sep 23, 2010 5:59 pm UTC
Forum: Mathematics
Topic: Convergence Problem
Replies: 13
Views: 2235

### Re: Convergence Problem

Hence, for large n , \left|\sec n\right| < cn^{13.65} for some constant c . (I've skipped many steps here, so I might be wrong, but if so, I'm pretty sure that I'm not very wrong.) As a result, it's certainly not exponentially large infinitely often, which it would need to be in order for the seque...
Thu Sep 23, 2010 6:03 am UTC
Forum: Mathematics
Topic: Convergence Problem
Replies: 13
Views: 2235

### Re: Convergence Problem

I am familiar with the identity cos(x)=.5(e^(xi)+e^(-xi)) . I apologize for not being familiar with LATEX. If I did my math correctly, the nth term can also be written as:
2/{[e^(1+i)]^n+[e^(1-i)]^n}
This is as far as I can go.
Thu Sep 23, 2010 3:44 am UTC
Forum: Mathematics
Topic: Convergence Problem
Replies: 13
Views: 2235

### Convergence Problem

The following series was brought to my attention recently, and I have no idea whether it converges or diverges: sum from n=0 to n=infinity of sec(n)*e^(-n) The argument of the secant function is in radians, of course. As such, the integer values of n make the terms behave strangely. I do not even kn...