Search found 3683 matches

by PM 2Ring
Tue Feb 17, 2009 5:04 pm UTC
Forum: Science
Topic: Sound in Space
Replies: 14
Views: 2725

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: 9809

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: 1947

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: 4428

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: 25881

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: 19799

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: 1005

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: 2992

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: 1005

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: 7229

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: 4428

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: 4902

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: 7229

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: 3306

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: 25881

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: 1796

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: 25881

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: 25881

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: 105645

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: 4902

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: 2264

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: 4465

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: 4428

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: 2264

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.
by PM 2Ring
Wed Feb 04, 2009 12:01 pm UTC
Forum: Coding
Topic: anything fundamentally wrong with...?
Replies: 26
Views: 2264

Re: anything fundamentally wrong with...?

is there anything fundamentally wrong with using commas to string together what would otherwise be separate statements and ending the "block" with a semi I'll admit I was tempted to do this a few times, when I was young & foolish. :) And lived to regret it... I recommend avoiding this...
by PM 2Ring
Tue Feb 03, 2009 2:11 am UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4428

Re: golden ratio proof

You may enjoy playing with the "Phibonacci" sequence Whoa... there's a part of me that wishes I did maths instead of physics... that is a very cool sequence. Now I'm trying to prove that the ratio of two adjacent Fibonacci numbers F(n)/F(n-1) approaches phi for n->infinity, but I am not s...
by PM 2Ring
Mon Feb 02, 2009 5:57 pm UTC
Forum: Mathematics
Topic: 1 + 1 = ?
Replies: 44
Views: 5726

Re: 1 + 1 = ?

I believe 1+1 was proven to be 2 around 1900 by Bertrand Russel. It was. I have a picture of his original work. Its a halarious paper long proof. He also spent a few hundred pages just laying the groundwork for it. Sort of. Russell & Whitehead were attempting to formalize mathematics, from the ...
by PM 2Ring
Mon Feb 02, 2009 5:42 pm UTC
Forum: Mathematics
Topic: Life and math
Replies: 21
Views: 2335

Re: Life and math

I reckon you ought to include as part of your presentation the Life form that generates the primes as a sequence of gliders. Another nice one is the recursive "unit cell": a Life form that simulates Life. It's probably more exciting than a simple Turing machine (although it pains me to say...
by PM 2Ring
Mon Feb 02, 2009 5:29 pm UTC
Forum: Mathematics
Topic: golden ratio proof
Replies: 15
Views: 4428

Re: golden ratio proof

You may enjoy playing with the "Phibonacci" sequence: \varphi^0 = 1 \varphi^1 = \varphi \varphi^2 = \varphi + 1 \varphi^3 = 2\varphi + 1 \varphi^4 = 3\varphi + 2 \varphi^5 = 5\varphi + 3 etc (Sorry about the poor formatting. I'd better learn some LaTex, I guess.:)) EDIT: This pic features ...
by PM 2Ring
Mon Feb 02, 2009 5:01 pm UTC
Forum: Mathematics
Topic: One of those questions on the philosophy of mathematics
Replies: 18
Views: 2628

Re: One of those questions on the philosophy of mathematics

The physical world can be modeled (to an extent) by mathematics. But conversely, the mathematical world can be modeled (to an extent) by physical objects. That doesn't mean that one is inherently more "real" than the other. To argue further, we need to define reality... It appears that man...
by PM 2Ring
Thu Jan 29, 2009 7:34 pm UTC
Forum: Science
Topic: Phase of one molecule
Replies: 14
Views: 1324

Re: State of one molecule

Temperature is usually defined as proportional to the mean kinetic energy of a whole bunch of molecules, so the temperature of a single molecule isn't well-defined, either. But I agree with the OP that the main issue is with the lack of intermolecular forces.
by PM 2Ring
Thu Jan 29, 2009 7:29 pm UTC
Forum: Science
Topic: Most silly "constant of nature"
Replies: 64
Views: 7308

Re: Most silly "constant of nature"

As long as we're being pedantic.... ... you can as easily have a mole of Carbon atoms as a mole of ping-pong balls... I doubt that. :) In theory, there is no difference between theory and practice. In practice, there is a huge difference between theory and practice. According to Wikipedia, the stan...
by PM 2Ring
Thu Jan 29, 2009 7:03 pm UTC
Forum: Mathematics
Topic: Favorite mental math tricks/shortcuts
Replies: 61
Views: 9655

Re: Favorite mental math tricks/shortcuts

(x^2 - y^2) = (x + y)(x - y) Very useful for the 10th graders I teach. I usually use this in the opposite direction. 17*13 = 15^2-2^2 = 221 Me, too. If you memorize the squares up to 25*25, and use a few other formulas, like (50 + x)^2 = (2500 + 100x +x^2) and (100 + x)^2 = (10000 + 200x + x^2) so ...
by PM 2Ring
Thu Jan 29, 2009 6:29 pm UTC
Forum: Science
Topic: After the big bang, where did pi, e and the rules originate?
Replies: 53
Views: 5478

Re: After the big bang, where did pi, e and the rules originate?

e, on the other had, is more "abstract" in the sense that we can't measure e like we measure pi. We can easily give a geometric definition for e. Draw the hyperbola xy = 1. The area under the branch in the ++ quadrant between x=1 & x=e is exactly one. And so is the area between x=e &a...
by PM 2Ring
Thu Jan 29, 2009 5:58 pm UTC
Forum: Science
Topic: Rapidly rotating wire
Replies: 52
Views: 3879

Re: Rapidly rotating wire

Alternatively, the problem can be analyzed in a rotating frame of reference centered on the wire's midpoint Can we? According to the OP: Lets say you have a long wire out in space, and you start spinning it very quickly around one end, so it looks sort of like a rope with a weight on the end being ...
by PM 2Ring
Thu Jan 29, 2009 5:39 pm UTC
Forum: Mathematics
Topic: objects that we'd like to hold, but can't in this universe
Replies: 41
Views: 6212

Re: objects that we'd like to hold, but can't in this universe

It's quite easy to make a flat model of a Klein bottle from paper & adhesive tape. Sure, it still self intersects, but you can cut it into a pair of Moebius strips with a pair of scissors. And regarding the projective plane, there are programs around that let you play with hyperbolic tessellatio...
by PM 2Ring
Thu Jan 29, 2009 5:06 pm UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 3308

Re: Interesting sequences

I second t0rajir0u's nomination of derangements. The concepts are fairly easy to explain, and you can show the connection between the total number of permutations of n items (= n!) and number of derangements (= !n) and their relationship with e. I also like his idea of Beatty sequences, and not just...
by PM 2Ring
Thu Jan 29, 2009 4:38 pm UTC
Forum: Mathematics
Topic: Can I have your prime number?
Replies: 30
Views: 4902

Re: Can I have your prime number?

I think it's interesting to look at the primes from a complex POV. The Gaussian integers (complex numbers of the form a + bi, where a & b are both integers) have unique factorization. All the normal primes of the form 4n+3 are still prime in the Gaussians, all other primes have a Gaussian factor...
by PM 2Ring
Tue Jan 27, 2009 5:08 pm UTC
Forum: Science
Topic: Is consuming DNA safe? (not what you think. perverts.)
Replies: 39
Views: 5711

Re: Is consuming DNA safe?

You have to be really careful. Things labeled "75% ethanol" often contain methanol, which you definitely don't want to consume. That depends where you live. Some denatured ethanol does contain methanol, but it's pretty rare in Australia these days, and only used in certain applications. M...
by PM 2Ring
Tue Jan 27, 2009 4:37 pm UTC
Forum: Mathematics
Topic: x - cos(x) = 0
Replies: 36
Views: 10581

Re: x - cos(x) = 0

Prof. Dottie Fixed and I think that's probably part of why the name is what it is. And my high school colleague never published his result, so his chance of glory was lost. Thus is the lot of the 'umble amateur. :) Speaking of iterating cos, Julia sets of complex trig functions can look quite prett...

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