Search found 3699 matches

by PM 2Ring
Fri Feb 20, 2009 5:03 pm UTC
Forum: Language/Linguistics
Topic: Isn't it ironic?
Replies: 17
Views: 3468

Re: Isn't it ironic?

The true irony in Alanis's song is the irony she wasn't actually going for, typified by her line "And yeah, I really do think" in a song in which she might have done well to think it through just a bit more. What is more ironic than a song called "Ironic" that is ironic because ...
by PM 2Ring
Fri Feb 20, 2009 12:57 pm UTC
Forum: Language/Linguistics
Topic: What is the best constructed language?
Replies: 75
Views: 19589

Re: What is the best constructed language?

So what's the difference between a conlang and a natural language? I assume that a natural language is one made over time, but doesn't that make every constructed language a natural language? According to evolutionary anthropologists, like Steve Pinker & Jared Diamond, natural languages are cre...
by PM 2Ring
Fri Feb 20, 2009 12:10 pm UTC
Forum: Language/Linguistics
Topic: To "that" or not to "that"
Replies: 32
Views: 3242

Re: To "that" or not to "that"

Slight thread hijack: http://uncyclopedia.wikia.com/wiki/That "That" is famous for being able to be repeated five times and still be grammatically correct, as in the phrase: "They say that that 'that' that that person said sounded dodgy". And http://www.jtbullitt.com/projects/tan...
by PM 2Ring
Fri Feb 20, 2009 9:14 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 488414

Re: Favorite math jokes

Do they serve beer in Klein steins at the Möbius strip club?
by PM 2Ring
Thu Feb 19, 2009 11:57 pm UTC
Forum: Mathematics
Topic: Calculus Homework: Integration
Replies: 9
Views: 2220

Re: Calculus Homework: Integration

Haha holy cow! thanks guys, I got it. Although, I'm a little ashamed to admit that last bit is a tad over my head. Appreciate your help! Sorry for the thread hijack, Enderb. I didn't mean to confuse you. Since your question had already been answered, I just thought I'd chuck in something interestin...
by PM 2Ring
Thu Feb 19, 2009 5:18 pm UTC
Forum: Mathematics
Topic: Calculus Homework: Integration
Replies: 9
Views: 2220

Re: Calculus Homework: Integration

The Wiki article has the famous e=\lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n However, it's not too hard to show that \lim_{n\to\infty} \left(1+\frac{1}{n - \frac{1}{2}}\right)^n converges much faster. But \lim_{n\to\infty} \left(1+\frac{1}{n - \frac{1}{2} + \frac{1}{12n}}\rig...
by PM 2Ring
Thu Feb 19, 2009 4:45 pm UTC
Forum: Mathematics
Topic: The Fibonacci Sequence
Replies: 14
Views: 3084

Re: The Fibonacci Sequence

Is there any practical use for it? I found it boring and a waste of my time. It wasn't a total waste of time: now you know you have no taste for number theory, and you should avoid it in future. :) IMHO, The Fibonacci sequence is a good introduction to number theory. But I understand that number th...
by PM 2Ring
Thu Feb 19, 2009 2:26 pm UTC
Forum: Science
Topic: What's your favorite element? and the one you hate the most?
Replies: 98
Views: 10026

Re: What's your favorite element? and the one you hate the most?

My least favorite is probably Bismuth because it is boring and Pepto-Bismol tastes awful. I suppose that depends on how you want to define "boring". While bismuth was traditionally regarded as the element with the heaviest stable isotope, bismuth-209, it had long been suspected to be unst...
by PM 2Ring
Thu Feb 19, 2009 2:19 pm UTC
Forum: Science
Topic: Something thats always confused me about "The 4th Dimension"
Replies: 35
Views: 3439

Re: Something thats always confused me about "The 4th Dimension"

If you ask any astrophysicist or semi-intellectual person what the fourth dimension is, they'll say that it's spacetime. But what has always confused me was the "geometrical" fourth dimension. What does this have to do with spacetime. "The Fourth Dimension" usually means time. T...
by PM 2Ring
Wed Feb 18, 2009 2:36 pm UTC
Forum: Mathematics
Topic: Proof (inequalities)
Replies: 17
Views: 1319

Re: Proof (inequalities)

t0rajir0u wrote:I'd avoid algebra altogether. The four points (0, 0), (b, a), (d, c), (b + d, a + c) form a parallelogram; what is the slope of the diagonal compared to the slope of the other two edges?

(By the way, you need non-strict inequalities.)


t0rajir0u wins!
by PM 2Ring
Wed Feb 18, 2009 2:23 pm UTC
Forum: Mathematics
Topic: Using Double-angle Formulas to Establish Identities
Replies: 11
Views: 2006

Re: Using Double-angle Formulas to Establish Identities

t0rajir0u wrote:Yep. It's possible to generalize that construction.

Thanks. That's the plan. But first I'm "warming up" by proving the formula for tan(nx). Conceptually it's easy (and so is tan(a+b+c+...)), but the notation gets rather messy. I might "cheat" & look at Wiki or Mathworld. :)
by PM 2Ring
Wed Feb 18, 2009 12:24 pm UTC
Forum: Coding
Topic: TI Basic Prime Factorer
Replies: 49
Views: 9940

Re: TI Basic Prime Factorer

Here's how I find all factors in Python. The mixed base counting iterator comes in handy for other permutation generator tasks, too. mbcount.py #! /usr/bin/env python ''' Mixed base counting iterator The digits are stored in a list, with the msd in the zeroth element. Initializer t is a list contain...
by PM 2Ring
Wed Feb 18, 2009 5:20 am UTC
Forum: Mathematics
Topic: Proof (inequalities)
Replies: 17
Views: 1319

Re: Proof (inequalities)

You're off with the Fareys. :)
by PM 2Ring
Wed Feb 18, 2009 5:03 am UTC
Forum: Science
Topic: What's your favorite element? and the one you hate the most?
Replies: 98
Views: 10026

Re: What's your favorite element? and the one you hate the most?

I have a teensy phosphor-coated vial of tritium, which is gradually losing it's glow. On the bright side, it's turning into helium 3. :) With a half-life of more than 10 years, that change should be almost imperceptible, unless you've had it for a long time. I wonder if it isn't leaking out. Wiki s...
by PM 2Ring
Wed Feb 18, 2009 4:55 am UTC
Forum: Science
Topic: Sound in Space
Replies: 14
Views: 2769

Re: Sound in Space

asad137 wrote:
PM 2Ring wrote:A sufficiently large & intense space explosion would be audible, due to gravity waves. :)


A spherically-symmetric time-dependent mass distribution does not produce gravity waves.

Asad

Granted, so the explosion I have in mind would be highly asymmetric.
by PM 2Ring
Wed Feb 18, 2009 4:44 am UTC
Forum: Mathematics
Topic: Using Double-angle Formulas to Establish Identities
Replies: 11
Views: 2006

Re: Using Double-angle Formulas to Establish Identities

Am I on the right track? Let \tan 3\theta = \tan 3x \tan 3\theta = \tan (3x + 2\pi k) k= 0,1,2 Thus \theta = x , x + 2\pi/3 or x + 4\pi/3 and \tan \theta = \tan x , \tan (x + 2\pi/3) or \tan (x + 4\pi/3) Let z = \tan \theta Let T_k = \tan (x + 2k\pi/3) z = T_0, T_1 or...
by PM 2Ring
Tue Feb 17, 2009 5:04 pm UTC
Forum: Science
Topic: Sound in Space
Replies: 14
Views: 2769

Re: Sound in Space

A sufficiently large & intense space explosion would be audible, due to gravity waves. :) And if a supernova goes off in your vicinity, I reckon the local density of hydrogen would be enough to carry some sound. After all, such explosions contribute to the birth of stars, due to the pressure wav...
by PM 2Ring
Tue Feb 17, 2009 4:40 pm UTC
Forum: Science
Topic: What's your favorite element? and the one you hate the most?
Replies: 98
Views: 10026

Re: What's your favorite element? and the one you hate the most?

All the inert gases have a mind-altering & anaesthetic effect at high enough partial pressure, even helium. The effect is very similar to that of nitrous oxide. When divers go too deep with normal air, they can experience this effect from nitrogen, and they refer to this effect as nitrogen narco...
by PM 2Ring
Tue Feb 17, 2009 6:04 am UTC
Forum: Mathematics
Topic: Using Double-angle Formulas to Establish Identities
Replies: 11
Views: 2006

Re: Using Double-angle Formulas to Establish Identities

metagross111 wrote:Establish the Identity:

tan(X) + tan(X + 120°) + tan(X + 240°) = 3tan(3X)

Cute! I see from playing with this formula in bc that it generalizes to other odd polygons. But how do we prove the general case?
by PM 2Ring
Sun Feb 15, 2009 9:52 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4516

Re: golden ratio proof

Here's a small article I wrote a few years ago, that I thought might be appropriate for this thread. ( And it gives me an opportunity to practice my newly-acquired LaTeX skills. :)) Fibonacci numbers, the Golden ratio phi, and Prèvost's Constant Introduction The Fibonacci sequence is generated as fo...
by PM 2Ring
Sun Feb 15, 2009 9:05 am UTC
Forum: Coding
Topic: Programs that print their own source code
Replies: 100
Views: 26281

Re: Programs that print their own source code

I'll post one or two in PostScript a bit later. I've got one in C here (written by someone else) that is also a palindrome! A PostScript program which outputs itself to the console: /s ( [(/s)<28>s<29>(def)s]{=}forall ) def [(/s)<28>s<29>(def)s]{=}forall And this PostScript one prints itself to the...
by PM 2Ring
Mon Feb 09, 2009 10:07 am UTC
Forum: Science
Topic: Realistic 'Planet Buster'
Replies: 257
Views: 20571

Re: Realistic 'Planet Buster'

you could have a gravity manipulator that quickly changes the direction of gravity crushing everything. No, because that's not Realistic. If we can use Un-Realistic means, then I vote for the Wunderland Treatymaker . The Wunderland Treatymaker was used only once. It was a gigantic version of what i...
by PM 2Ring
Mon Feb 09, 2009 10:01 am UTC
Forum: Science
Topic: Help please: Binding energy
Replies: 8
Views: 1038

Re: Help please: Binding energy

On a slight tangent, is there a formula for determining the number of neutrons in stable isotopes, given the atomic number? Ideally, something that doesn't have 90 parameters. :) I tried using least squares techniques & found a degree 5 polynomial, but it's not very good. Have you met the SEMF?...
by PM 2Ring
Mon Feb 09, 2009 9:52 am UTC
Forum: Science
Topic: Charged Black Hole
Replies: 27
Views: 3125

Re: Charged Black Hole

What wisnij said also applies to how the black hole's gravity "gets out". From http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html How does the gravity get out of the black hole? Purely in terms of general relativity, there is no problem here. The gravity doesn't...
by PM 2Ring
Sun Feb 08, 2009 9:23 am UTC
Forum: Science
Topic: Help please: Binding energy
Replies: 8
Views: 1038

Re: Help please: Binding energy

On a slight tangent, is there a formula for determining the number of neutrons in stable isotopes, given the atomic number? Ideally, something that doesn't have 90 parameters. :) I tried using least squares techniques & found a degree 5 polynomial, but it's not very good.
by PM 2Ring
Sun Feb 08, 2009 8:48 am UTC
Forum: Mathematics
Topic: The probability of impossible
Replies: 63
Views: 7406

Re: The probability of impossible

\begin{align*} 1 &= P\left(\bigcup_{i\in\mathbf{N}} A_i\right) \\ &= \sum_{i\in\mathbf{N}} P(A_i) \\ &= \sum_{i\in\mathbf{N}} \epsilon\end{align*} That final sum diverges for all \epsilon\in [0,1] except 0, and in that case the equality is violated. So, one of my assumpt...
by PM 2Ring
Sun Feb 08, 2009 6:58 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4516

Re: golden ratio proof

Huh. For some reason I'd never come across that back when I was fiddling more with it. I probably just assumed it wouldn't do it properly because white is just treated as rgb instead of a spectrum, but yeah, obviously it could still stimulate spectrum effects when it "knows" you want whit...
by PM 2Ring
Sun Feb 08, 2009 6:36 am UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 5005

Re: Can I have your prime number?

http://en.wikipedia.org/wiki/Heegner_number Euler's prime-generating polynomial n 2 + n + 41, which gives (distinct) primes for n=0, ... 39, is related to the Heegner number 163. In number theory, a Heegner number is a (square-free) positive integer d such that the imaginary quadratic field \mathbf...
by PM 2Ring
Sun Feb 08, 2009 6:28 am UTC
Forum: Mathematics
Topic: The probability of impossible
Replies: 63
Views: 7406

Re: The probability of impossible

Thanks, Office. I was starting to question my understanding of ... lots of things. You say that like it's a bad thing. That's hardly in the spirit of your Feynmann quote. :) Really? Why can't I pick a random integer, or a random rational between 0 and 1? Is there some measure-theoretic thing I'm mi...
by PM 2Ring
Sun Feb 08, 2009 5:42 am UTC
Forum: Mathematics
Topic: taylor expansion of sin(x)
Replies: 15
Views: 3376

Re: taylor expansion of sin(x)

Cool! My question was essentially answered. What I should've said in the first was that cos and sin were the only trigonometric functions that cycled through each other(I doubt you can manipulate e^x's Taylor series into a trig function without a trig function). Actually you can, using complex numb...
by PM 2Ring
Sun Feb 08, 2009 4:59 am UTC
Forum: Coding
Topic: Programs that print their own source code
Replies: 100
Views: 26281

Re: Programs that print their own source code

Ended wrote:...I don't think reading in and printing the source file is quite in the spirit of the challenge.

Indeed.

jaap wrote:
Xanthir wrote:You're looking for the term 'quine'. There are a bunch of them out there. ^_^


Such as in this thread in the computer science forum.

Thanks, guys.
by PM 2Ring
Sat Feb 07, 2009 6:22 pm UTC
Forum: Science
Topic: tricked out bottle rocket, or sinker?
Replies: 15
Views: 1870

Re: tricked out bottle rocket, or sinker?

Thus the ideal fuel would be molten uranium. Why not molten iridium or osmium? Uranium may have a high atomic mass, but it's certainly not the densest element. Slightly more seriously, I suppose liquefied air (or at least nitrogen) would also not be in keeping with the spirit of the assignment. And...
by PM 2Ring
Sat Feb 07, 2009 5:33 pm UTC
Forum: Coding
Topic: Programs that print their own source code
Replies: 100
Views: 26281

Re: Programs that print their own source code

You're looking for the term 'quine'. There are a bunch of them out there. ^_^ "To quine a phrase", to quine a phrase. :) I was introduced to W. V. O. Quine via Godel, Escher, Bach, which I recently started re-reading. But I didn't realize the term "quine" has become common jargo...
by PM 2Ring
Sat Feb 07, 2009 5:09 pm UTC
Forum: Coding
Topic: Programs that print their own source code
Replies: 100
Views: 26281

Programs that print their own source code

It can be a fun exercise to write a program that prints its own source code. It gets you thinking about the language syntax in ways that are a bit different to the usual programming problems. I couldn't find a thread on this topic here, so I thought it might be a nice idea to create one where we can...
by PM 2Ring
Sat Feb 07, 2009 4:54 pm UTC
Forum: Mathematics
Topic: How many digits of Pi do you know?
Replies: 445
Views: 107030

Re: How many digits of Pi do you know?

3.141592653589793238462643383279502 8 8 Fixed ;) I noticed a few other mistakes while reading this thread. It's not often I find a use for the hundred digits I know. :) Maybe someone could write a script to check these posts for errors, and create a nice little report. I learned the first few digit...
by PM 2Ring
Sat Feb 07, 2009 3:53 pm UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 5005

Re: Can I have your prime number?

There's a nice prime counting formula, due to Riemann IIRC, that uses the (ordinary) zeta function. I coded this formula in C years ago. Here it is, in case anyone's curious. /* * R I E M * * A function found by Riemann for Pi(x), the number of primes <= x. * * These are the formulae, using a modif...
by PM 2Ring
Sat Feb 07, 2009 3:43 pm UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2332

Re: anything fundamentally wrong with...?

Berengal wrote:Asserts are usually conditionally defined, so in release code it's nothing.


Exactly. So thinking of them as C's version of try...catch is somewhat misleading.
by PM 2Ring
Sat Feb 07, 2009 3:35 pm UTC
Forum: Science
Topic: Organic Vegetables
Replies: 73
Views: 4542

Re: Organic Vegetables

http://www.dhmo.org/ Welcome to the web site for the Dihydrogen Monoxide Research Division (DMRD), currently located in Newark, Delaware. The controversy surrounding dihydrogen monoxide has never been more widely debated, and the goal of this site is to provide an unbiased data clearinghouse and a ...
by PM 2Ring
Sat Feb 07, 2009 10:58 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4516

Re: golden ratio proof

Are the colors in there due to colored lights, or has POV-Ray gotten sophisticated enough to model prisms? POV-Ray has been able to model dispersion for a while now, but it does slow down rendering a bit, as it has to trace more rays, so I rarely use this feature, and when I do I don't use many dis...
by PM 2Ring
Sat Feb 07, 2009 10:15 am UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2332

Re: anything fundamentally wrong with...?

Asserts should not be active once the program has been released. They should only be active during the development phase.

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