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You can do it this way, but it could involve too many calculations and therefore might not be useful in practice. In this example, you would have to calculate the probability of exactly 2 people sharing a birthday, of exactly 3 sharing a birthday, 4 sharing a birthday, and so on, and add them all up – too much work, wouldn’t you agree? Much simpler to just calculate the probability for no shared birthday and subtract from 1.
The classic bird joke:
Q: Why is there no painkillers in the bird jungle?
A: Because the parrots-ate-em-all!
At any rate it's most often told bird joke here in the UK, where the most common pain-relief tablets people take are called Paracetamol.
Ciao Libera!
Io sono inglese, vivendo a Londra, e studio l’italiano da quindici anni; mi piace molto questa bella lingua. Ho diversi amici italiani a Londra e mi piace parlare con loro in italiano.
Credo che una versione italiana di questo sito sarebbe un’ottima idea!
Un saluto.
Q: What happened to the guy who didn’t believe in electricity until one day he touched the “plus” terminal of a high-voltage D.C. power source?
A: He was positively shocked.
Q: What radio station do chemists like to listen to?
A: 100 Fm.
(Fermium has atomic number 100.)
Q: What music do mathematical lumberjacks listen to?
A: Logger-rhythm & blues.
And I get …
[list=*]
[*]
… tada! Is it right? Is it? Yes, I’m very sure it is.
Let me check … first:
[list=*]
[*]
so it is indeed a unit vector. Now
s0 DÔA = CÔD. And … drum roll …
– so CÔA = 2·DÔA = 2·CÔD!
YES!!
Ah, ah, ah. We want a unit vector, so we can straightaway take √(x²+y²+z²) = 1 – no need to mess around with ugly expressions! Why didn’t I think of that before?
This means my equation [1] in post #12 becomes
[list=*]
[*]
Also from post #12,
[list=*]
[*]
From the previous post,
[list=*]
[*]
Now we can solve for everything!
Okay, let me try something else. I will assume OC to be in the plane formed by OA and OD and let (r,s,t) be a nonzero vector perpendicular to this plane. We have
[list=*]
[*]
which leads, on eliminating s and t, to
[list=*]
[*]
Now we can’t have r = 0, otherwise s = t = 0 as well. Therefore:
[list=*]
[*]
Now substitute for z from my previous post and we can pin down x and y a bit more.
… to be continued.
My life is just like English grammar. Although the past might be irregular, the present is perfect and so I need not be tense about the future.
so C would be the answer for division by (x+1).
They say, “Don’t get mad, get even.” I say: “Don’t get mad, get even madder.”
—Vinnie Jones
ganesh wrote:If you can stay calm while all around you is chaos, then you probably haven't completely understood the situation.
* * *But sometimes ignorance is a bliss!
I agree. If it’s situation you don’t need to get involved in, there’s no need to poke your nose in it and be a busybody. Just step out of the chaos and let others deal with it.
Q: Why do geometers never get lost?
A: Because they can use compasses.
* * *
Q: How did the awkward mathematician go off?
A: At a tangent.
A deep one:
Q: How do you make an ideal principal?
A: Be a model headmaster.
(You may not get it if you aren’t familiar with principal ideals in ring theory.)
And how do I work E=mc² into it?
It comes from the formula for relativistic momentum:
[list=*]
[*]
where p is momentum and m₀ is rest mass. Simply put p = 0 for a particle at rest.
The approximation of x is supposed to be -2, actually, but for unknown reasons the negative sign can't show up in LaTeX.
That’s because you put a backslash before the - sign.
\lim_{x\to\-2}
Don’t put any backslash: it’s just
\lim_{x\to-2}
On the other hand, do put a backslash before the cos – otherwise cos in italics looks like a product of three variables. When formatted properly, the expression should look like this:
[list=*]
[*]
PS: I looked through your working; I should think what you did was just fine.
It’s a good article. Here are a few of my suggestions.
Firstly, I think the little story between Alex and Sam can be omitted. I don’t see how it’s relevant to relativity – more like having to do with theories of expanding space (e.g. by viewing 3D space as embedded in a larger 4d hyperspace – much like the 2D surface of a sphere is embedded in 3D space).
Secondly, I would mention that things like length and mass also depend on speed: the faster an object moves relative to an observer, the shorter (in the direction of motion) and more massive the observer will measure it to be.
And thirdly, you didn’t mention the most famous equation in all of physics: E = mc²! Most people who are not familiar with special relativity may still be familiar with this equation, so I think it would be a give them some background information on it.
Never fight fire with fire. Always fight fire with water. It’s more effective.
***
Like attracts like. (With the exception of electric charges and magnetic poles.)
***
Be a member of the Self Preservation Society: do whatever it takes to stay alive, even if it kills you!
***
I don’t think induction is the way to go about proving this. Better to argue directly as follows.
The product is clearly divisible by 2, since at least one of n, n+1, n+2 is even (you can’t have three consecutive odd integers).
Also, any three consecutive integers must contain a multiple of 3. One way to prove this is to reduce mod 3:
[list=*]
[*]If n ≡ 0 (mod 3) then n is divisible by 3.
If n ≡ 1 (mod 3) then n+2 is divisible by 3.
If n ≡ 2 (mod 3) then n+1 is divisible by 3.[/*]
[/list]
Since n , n+1, n+2 contain a multiple of 2 and 3, and gcd(2,3) = 1, their product is divisible by 2×3 = 6.
Thanks for your replies.
I don’t know what I’ve done but I hope it’s nothing wrong. For the moment I can get around using a proxy server. I just have to be extra cautious now or the proxy will get banned as well!
Sorry, I meant to say 3x = 90°, so yes, x = 30°.
Similar to ganesh’s “Miscellany” thread except that these interesting jewels of knowledge are short (one sentence long).
[list=1]
[*]The Black Poplar (Populus nigra) is a declining species of tree in Britain but a rare native specimen can be found at Hainault Forest Country Park, Greater London / Essex.
http://speakforum.forumotion.com/t42-trees
[/*]
[*]The philosophical term Angst was coined by Søren Kierkegaard, a Christian existentialist philosopher.
http://speakforum.forumotion.com/t35-existentialism#105
[/*]
[*]The set of all intervals on the chromatic scale, categorized by the number of semitones between the first and last notes modulo an octave, together with the operation of “addition” defined by adding their constituent semitones, forms a cyclic group of order 12.
http://speakforum.forumotion.com/t34-acoustics#102[/*]
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