Search found 3699 matches

by PM 2Ring
Wed Mar 04, 2009 7:06 am UTC
Forum: Science
Topic: Trip to the moon [Homework problem]
Replies: 21
Views: 4764

Re: Trip to the moon [Homework problem]

You can counter gravity by aiming the engines away from the direction of motion. "Straight line" is a difficult concept in any case: under relativity, a straight line from A to B is usually defined as "the path a photon would have taken". Fair call. We really should use Minkowsk...
by PM 2Ring
Wed Mar 04, 2009 6:54 am UTC
Forum: Science
Topic: What's your favorite element? and the one you hate the most?
Replies: 98
Views: 10047

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

Liquid mercury isn't as dangerous as the vapour or mercury salts, but it's still not a good idea to play with it. But we didn't know how bad it was back in the Dark Ages, when I was a teenager, and I had a small mercury collection for several years. I'd occasionally pour some into the palm of my han...
by PM 2Ring
Wed Mar 04, 2009 6:39 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2009576

Re: Coding: Fleeting Thoughts

Is there a place on these forums for posting source code of small games, puzzles & toys? For example, a few months ago I wrote a Python program that generates Apollonian Gaskets (GUI using GTK), and I think some people here may enjoy playing with it (and modifying it). Another Python toy lets yo...
by PM 2Ring
Wed Mar 04, 2009 6:23 am UTC
Forum: Science
Topic: Plants can graft themselves in nature?
Replies: 8
Views: 2039

Re: Plants can graft themselves in nature?

We had a tree at my high school that had joined two of its branches into a loop. Clearly, it knew nothing of graph theory. :) Sorry, I can't remember the species, I think it may have been a eucalypt. All I can recall is that it had reddish bark.
by PM 2Ring
Wed Mar 04, 2009 6:13 am UTC
Forum: Science
Topic: Trip to the moon [Homework problem]
Replies: 21
Views: 4764

Re: Trip to the moon [Homework problem]

Goemon wrote:Eh? Why infinite?


Gravity. Even for photons the path is slightly bent.

When traveling through the solar system, any path is an orbit with respect to the Sun. Of course, when the thrusters are firing, this is modified a bit, but not enough to allow a straight line path.
by PM 2Ring
Tue Mar 03, 2009 5:16 pm UTC
Forum: Science
Topic: Demonstrations for kids
Replies: 14
Views: 1540

Re: Demonstrations for kids

For biology-related experiments, you could do the old celery stalks in dyed water trick, to show how the dye gets carried up the celery, or you could do any number of microscope demonstrations. Rather than using celery, I suggest cauliflower, as it's easier to see the dye. Plus, it's a fractal. :) ...
by PM 2Ring
Tue Mar 03, 2009 5:08 pm UTC
Forum: Science
Topic: What's your favorite element? and the one you hate the most?
Replies: 98
Views: 10047

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

Allenr wrote:I hated Iron because of its multiple oxidation levels.

I take it you don't like Chromium much, in that case, despite all the pretty colours. :)
by PM 2Ring
Tue Mar 03, 2009 5:05 pm UTC
Forum: Science
Topic: Breathing Water - At all possible?
Replies: 25
Views: 2831

Re: Breathing Water - At all possible?

So what would be good for some sort of weird mutant human? Giant frilly frond things? That doesn't sound very practical (although it'd look good in a sci-fi movie): they'd be unwieldy, and prone to attract things that'd want to nibble on them. Large gilled creatures like sharks need to keep moving ...
by PM 2Ring
Tue Mar 03, 2009 3:55 pm UTC
Forum: Language/Linguistics
Topic: Little editing/grammar mistakes that drive you up the wall
Replies: 784
Views: 110797

Re: Little editing/grammar mistakes that drive you up the wall

^ That is slightly strange, but it strikes me as sort of...properising them. Making the vague concepts of life and liberty into specific values entitled Life and Liberty...much like the one people seem to do a lot on the net recently: "This is a Good Thing." <^> I'm somewhat fond of the o...
by PM 2Ring
Tue Mar 03, 2009 12:30 pm UTC
Forum: Science
Topic: Trip to the moon [Homework problem]
Replies: 21
Views: 4764

Re: Trip to the moon [Homework problem]

"A spaceship is on a straight line path between the earth and the moon. At what distance from the earth is the net gravitational force on the spaceship zero" I realize this is just a homework problem, but I don't think I'd like to be on such a rocket: the g-force would be horrendous! At l...
by PM 2Ring
Tue Mar 03, 2009 10:26 am UTC
Forum: Mathematics
Topic: Sum of Corners
Replies: 11
Views: 1461

Re: Sum of Corners

To be honest, I haven't ever heard of a regular polyhedron made out of hexagons, [...] or there is no polyhedron that can be made out of hexagons (I doubt the last one though) How would you build one? You need at least 3 polygons meeting at each vertex to form a solid. Each hexagon has vertices of ...
by PM 2Ring
Tue Mar 03, 2009 10:04 am UTC
Forum: Mathematics
Topic: Gauss v Euler
Replies: 48
Views: 17309

Re: Gauss v Euler

Gauss for quality, Euler for quantity. But I'm also a big Ramanujan fan. Galois died too young; those French cigarettes are pretty strong.... :) Anyway, these sorts of questions are difficult to answer, since the later guys mostly had access to the earlier guys' results. Ramanujan is a bit of an exc...
by PM 2Ring
Tue Mar 03, 2009 6:48 am UTC
Forum: Mathematics
Topic: Using Double-angle Formulas to Establish Identities
Replies: 11
Views: 2012

Re: Using Double-angle Formulas to Establish Identities

Ok. Here's the generalization, and a variant for even n as well (I didn't bother checking Wiki, etc). First, I'll prove the formula for tan(nx). Given \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} Find the formula for tan(nX), where n is a positive integer Let P_k(n) = \su...
by PM 2Ring
Tue Mar 03, 2009 4:54 am UTC
Forum: Science
Topic: Nonlinear spacetime?
Replies: 14
Views: 1825

Re: Nonlinear spacetime?

Would we know if it did? We don't really have anything to compare time to, and on our timescales as well as in our gravity well, the curvature in time required to make it a loop could be inperceivable. Or does the math create phenomena that definitely deviate from our perception of reality? Fair ca...
by PM 2Ring
Sun Mar 01, 2009 5:33 pm UTC
Forum: Mathematics
Topic: Number of primes...
Replies: 8
Views: 1414

Re: Number of primes...

I recently posted a C program here that approximates the prime counting function, if you're interested. Can I have your prime number? Here is the function compared to some actual values of Pi(x): The distribution of primes -------------------------- x Pi(x) Riemann(x) 1E1 4 5 1E2 25 ...
by PM 2Ring
Sun Mar 01, 2009 5:20 pm UTC
Forum: Mathematics
Topic: Proof that the sqrt of 2 is irrational?
Replies: 28
Views: 3996

Re: Proof that the sqrt of 2 is irrational?

Since we're using the FTA, we can avoid the use of proof by contradiction. If p/q is a fraction in its lowest terms, with q not equal to one, then so is \left(\frac{p}{q}\right)^n , where n is an integer not equal to zero. So no such fraction p/q is the nth root of an integer. QED But do we ...
by PM 2Ring
Sun Mar 01, 2009 4:37 pm UTC
Forum: Science
Topic: LHC Dangerous?
Replies: 372
Views: 88210

Re: LHC Dangerous?

Why did people think the micro black holes would kill us? Did they not believe in Hawking radiation Well, micro black holes can only last long enough to do anything if Hawking radiation doesn't happen, or at least if it works differently than expected, eg due to string theory related effects. So th...
by PM 2Ring
Sun Mar 01, 2009 4:30 pm UTC
Forum: Science
Topic: Light Enigma
Replies: 38
Views: 3501

Re: Light Enigma

The planck time defines a regime, not a fundamental length scale. When you get down to the planck time, you expect quantum gravity to be important. What happens at that scale is not known, and it's also not known if it's going to happen specifically at that scale. It's actually most like the scale ...
by PM 2Ring
Sun Mar 01, 2009 3:16 pm UTC
Forum: Language/Linguistics
Topic: To "that" or not to "that"
Replies: 32
Views: 3255

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

gmalivuk wrote:To have froken out, though, makes sense to me!


Thus spake gmalivuk.

:)
by PM 2Ring
Sun Mar 01, 2009 2:30 pm UTC
Forum: Language/Linguistics
Topic: What is the best constructed language?
Replies: 75
Views: 19620

Re: What is the best constructed language?

In the context of this thread, do reconstructed languages count as constructed languages? I reckon it'd be cool to learn Proto Indo-European. If my brain was a bit younger. :) I agree that Esperanto is probably the most practical constructed language to learn. I started to teach myself Esperanto whe...
by PM 2Ring
Thu Feb 26, 2009 3:21 pm UTC
Forum: Coding
Topic: Can comments affect performance?
Replies: 19
Views: 3559

Re: Can comments effect performance?

PostScript also has special comments that are used for document structuring, so they may be analyzed depending on what sort of interpreter is parsing the program. http://en.wikipedia.org/wiki/Document_Structuring_Conventions Document Structuring Conventions, or DSC, is a set of standards for PostScr...
by PM 2Ring
Thu Feb 26, 2009 12:17 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 489804

Re: Favorite math jokes

Did the Ancient Romans refer to the 69 position as a 59?
by PM 2Ring
Thu Feb 26, 2009 10:20 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2009576

Re: Sacrificing many chickens to the computing gods: Fleeting Th

I hope the idiot who has hacked these forums gets a visit from The BHM. Soon. [url]<a class="linkification-ext" href="http://www.xkcd.com/542/" title="Linkification: http://www.xkcd.com/542/">http://www.xkcd.com/542/</a>[/url] You'd have to have less neural matter than...
by PM 2Ring
Thu Feb 26, 2009 7:47 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2009576

Re: Sacrificing many chickens to the computing gods: Fleeting Th

I hope the idiot who has hacked these forums gets a visit from The BHM. Soon. http://www.xkcd.com/542/ You'd have to have less neural matter than a nematode to be amused by performing this kind of stunt, IMNSHO. There's a lot of great material here that's been ruined. I hope there's a backup...
by PM 2Ring
Wed Feb 25, 2009 3:19 pm UTC
Forum: Language/Linguistics
Topic: What is the best constructed language?
Replies: 75
Views: 19620

Re: What is the best constructed language?

Ok, it's not the ancestral form, but Devanagari is ultimately a cursive descendant of Brahmi. From my previous link: The Nāgarī or Devanāgarī alphabet descended from the Brahmi script sometime around the 11th century AD. It was originally developed to write Sanskrit but was later adapted to write ma...
by PM 2Ring
Wed Feb 25, 2009 3:07 pm UTC
Forum: Science
Topic: Speed of a photon < c?
Replies: 8
Views: 1178

Re: Speed of a photon < c?

http://en.wikipedia.org/wiki/Quantum_electrodynamics#Physical_interpretation_of_QED In classical optics, light travels over all allowed paths and their interference results in Fermat's principle. Similarly, in QED, light (or any other particle like an electron or a proton) passes over every possibl...
by PM 2Ring
Wed Feb 25, 2009 2:33 pm UTC
Forum: Science
Topic: Speed of a photon < c?
Replies: 8
Views: 1178

Re: Speed of a photon < c?

We can take the simple approach, and say that a photon is emitted by atom A, travels at c in a straight line, and is absorbed by atom B. But if we start talking about virtual particle production, then we get photons that don't travel in straight lines, and that propagate at speeds lower or higher th...
by PM 2Ring
Wed Feb 25, 2009 2:16 pm UTC
Forum: Mathematics
Topic: Homework: I am stuck regarding Geometric Mean in Triangles
Replies: 11
Views: 890

Re: Homework: I am stuck regarding Geometric Mean in Triangles

Umm, try thinking of values that follow this: (X+a)(X+b)=0 Think of something that will fill in A and B. Do you understand? Hint: think of ways you can multiply whole numbers to get -36. (Am I doing this right?) Looks ok to me, except you changed a & b into A & B. Also, (x-a)(x-b) = 0 would...
by PM 2Ring
Wed Feb 25, 2009 2:03 pm UTC
Forum: Mathematics
Topic: Homework: I am stuck regarding Geometric Mean in Triangles
Replies: 11
Views: 890

Re: Homework: I am stuck regarding Geometric Mean in Triangles

You should be able to solve x2 + 5x - 36 = 0 by factoring, there's no need to resort to the quadratic formula. Note: only one solution of this equation will be physically meaningful.
by PM 2Ring
Wed Feb 25, 2009 12:43 pm UTC
Forum: Mathematics
Topic: Calculating Sine
Replies: 4
Views: 751

Re: Calculating Sine

A simple, accurate and efficient method is to use a recurrence relation that halves the argument repeatedly FWIW, this technique can be used with the arctan function to calculate pi (although there are much faster methods, of course). To approximate sin(x) I sometimes use \sin x \approx x\frac{12-x...
by PM 2Ring
Wed Feb 25, 2009 12:24 pm UTC
Forum: Mathematics
Topic: Prove room of 23 have 50% chance of sharing a birthday
Replies: 17
Views: 2244

Re: Prove room of 23 have 50% chance of sharing a birthday

What's the best way to handle the 29th of February in this problem, assuming uniform distribution of births? And assuming the Julian Calendar leapyear rule, although use of the Gregorian will give you extra credit. :)
by PM 2Ring
Wed Feb 25, 2009 12:07 pm UTC
Forum: Language/Linguistics
Topic: What is the best constructed language?
Replies: 75
Views: 19620

Re: What is the best constructed language?

With Tolkein, didn't the language come first, with the books just a place to use it? Wouldn't calling them "artistic" be backwards? The language was still created with artistic style in mind, in its word structure and grammar. I believe that's at least a large part of what people mean whe...
by PM 2Ring
Wed Feb 25, 2009 11:46 am UTC
Forum: Science
Topic: You have a barometer...
Replies: 30
Views: 4058

Re: You have a barometer...

And where are you going to find a nonelastic rope?! It was an impulse buy at the Ideal Physics Store... we were there buying the perfect barometer and ideal pressure-gradiated atmosphere that the traditional answer to the puzzle required, and saw the inelastic rope on the rack by the register, and....
by PM 2Ring
Wed Feb 25, 2009 11:32 am UTC
Forum: Mathematics
Topic: LaTeX and other markup!
Replies: 73
Views: 35697

Re: LaTeX and other markup!

It appears that the forum software doesn't support the \binom tag. What's the preferred form for binomial coefficients here? n \choose k , {}^n \! \mathbf{C}_k or {}_n \! \mathbf{C}_k ? I originally learned the 2nd form, though I'm quite familiar with the first form, and it's obviously the easiest t...
by PM 2Ring
Sun Feb 22, 2009 7:34 am UTC
Forum: Science
Topic: Nonlinear spacetime?
Replies: 14
Views: 1825

Re: Nonlinear spacetime?

Kurt Gödel found an interesting solution to the Einstein field equations which contains closed timelike curves, but it's not expected that this solution is physically realizable. It certainly doesn't apply to the universe we inhabit. http://en.wikipedia.org/wiki/G%C3%B6del_metric The Gödel metric is...
by PM 2Ring
Sun Feb 22, 2009 6:32 am UTC
Forum: Mathematics
Topic: Straightedge and graph paper geometry
Replies: 25
Views: 2602

Re: Straightedge and graph paper geometry

Even though I bet using the straightedge as a compass was cheating. Yeah, it was. Using stuff like this you can trisect an angle with straightedge and compass. Indeed. "Eyeballing" the straightedge is equivalent to having a marked straightedge. Also, the compass used in traditional straig...
by PM 2Ring
Sun Feb 22, 2009 4:58 am UTC
Forum: Mathematics
Topic: Calculus Homework: Integration
Replies: 9
Views: 2225

Re: Calculus Homework: Integration

I saw the function f(x) = ln(x) defined as \int\limits_{1}^{x}\frac{1}{x} in my Calculus class. That's evil. Did a man in a black hat attempt to kill that teacher? :) They should've said \ln x = \int\limits_{1}^{x}\frac{du}{u} Let x = r^n . Then \sum_{i=0}^{n-1} \left(r^{i+1} - ...
by PM 2Ring
Sun Feb 22, 2009 4:04 am UTC
Forum: Coding
Topic: Game of Life question
Replies: 15
Views: 1664

Re: Game of Life question

Two arrays are really only necessary if you are using bit arrays to hold the cells. If you're using integers, then you can use the same scheme as the original Scientific American Mathematical Games article. Each cell has 4 states: 0=dead, 1=alive, 2=dying, 3=birth. Of course, this requires an extra ...
by PM 2Ring
Sun Feb 22, 2009 3:34 am UTC
Forum: Science
Topic: Sun-powered device converts CO2 into fuel
Replies: 39
Views: 3377

Re: Sun-powered device converts CO2 into fuel

In fact, converting CO2 to methane before sequestering it would be far worse than sequestering the CO2 itself, because methane is a much more effective greenhouse gas. Using the methane as fuel is the only option here--and that's a rather roundabout method of getting solar power. As others have men...
by PM 2Ring
Fri Feb 20, 2009 6:10 pm UTC
Forum: Science
Topic: You have a barometer...
Replies: 30
Views: 4058

Re: You have a barometer...

If the barometer is the spring type, first measure the volume of the spring. Then draw it out into a long wire of uniform cross section until it's length equals the building height. Divide the volume by the cross sectional area to obtain the height of the building. If it's a mercury barometer, a sim...

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