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I choose a random number p_1 \in [0,1) and a subsequent series of (increasingly smaller) random numbers p_i \in [0, p_{i-1}). Then I can calculate the sum \sum_{i=1}^\infty p_i. Naturally, this sum is dependent on the random numbers chosen, so its particular result is not very insightful...

I was wondering someting that is so simple that it baffled me... When I have the equation a x^2+b x+c=0 this obviously has the solutions x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} And when I have the equation b x+c=0 this has the solution x=\frac{-c}{b} My problem now is the limiting case...

Another "play with numbers" website http://digicc.com/fido/ It's probably related to the fact that we have a base-10 number system, but I fail to see how it works... This website does the following: 1) You write down a 3 or 4 digit number, say X=x1 x2 x3 x4 (where the x's denote the...

I've got a horrible system of 8 coupled differential equations: \frac{\partial}{\partial t} N_0=-R_{0,2}N_0Y_1+\sum_{j=1}^5W_{j,0}N_j-C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial t} N_1=-R_{1,3}N_1Y_1-W_{1,0}N_1+W_{2,1}N_2+W_{4,1}N_4+C_{0,1}^{4,2}N_0N_4 \frac{\partial}{\partial...

Hi! I have a beautiful picture of some interaction that I want to explain with the standard model. I think it's probably a famous one, but I have no idea where & when I found it. If anybody recognises this data, then I'd be very happy to hear what it is... For now, I am guessing something...

I was wondering: why is the SM always written with a Lagrangian? Couldn't you just as well write it with a Hamiltonian? The way I understand, the Lagrangian gives me the kinetic energy minus the potential energy (basically a measure for the "free energy", though not in the thermodynamical...

"Extended" Fermat's last theorem. Just to satisfy my own curiousity: FLT states that there are no n\in{\mathbb N} such that x^n+y^n=z^n whenever n\geq 3 and x,y,z\in{\mathbb N}. However, what would happen when I allow n to be non-integer as well? Are there solutions if n\in{\mathbb...

I have three angular momenta l_1,l_2,l_3 which I want to couple into one big one: L\equiv l_1+l_2+l_3. Can I just do this by coupling l_1,l_2 into L' and then couple L',l_3 into L? I would guess that I could equally couple l_2,l_3 into L' and then couple l_1,L' into L and this would...

Hi all, I have been asked to give an informal presentation on the Standard Model to some chemists (note that this is not really my field of expertise ). I was wondering if there are some good (powerpoint) presentations out there that I could use to base mine on. That would save me a lot of...

Don't worry, I am not planning on starting another discussion about this topic! I was just curious to see what the opinions on this forum are. I really tried to write all the answers as objectively and clearly as possible and I did not intend to insult or provoke anybody. The order in which I...

I had a nice argument with someone who said roughly the following: - Fact: All succesful companies pay high salaries. - Fact: My company is not succesful. - Therefore: the company should increase salaries. To me this is obvious nonsense. However, I found it difficult to logically point...

As promised in another thread: Riddle me this, riddle me that... There are two carts on the table. For each cart, there is a rope attached on one side to the cart and via a pulley it is hanging over the edge of the table. On the other end of one rope a 5 kg weight is attached and on the other...

It seems like a simple question, but I get the feeling that there is a catch: You are standing on a plate attached to a pulley. The rope through the pulley is attached to the ceiling with one end and you pull on the other end. Can you lift the plate and yourself? a. Yes, but only the...

Maybe most of you have seen this before, but I find it cool and that's why I thought I share it with you. :smile: Lets look at the sum \sum_{p\leq N}\frac{1}{p} where p represents only prime numbers. If I calculate the value for this sum when taking into account all prime numbers < 105...

I just learned something really cool. Choose 13 real numbers x_1,x_2,\ldots,x_{13}\in\mathbbb{R} with x_i\neq x_j if i\neq j. For these 13 numbers there exist at least two numbers amongst them such that 0 \; < \; \frac{x_i-x_j}{1+x_ix_j} \; \leq \; 2-\sqrt{3} Isn't that cool?! (I...

Check this out: http://www.ode.nl/scripts/article.php?aID=3773 Lots of really deep misunderstanding of physics! :wink: My favourite part: So yeah, I guess that the zero point field (I'm assuming they are talking about the non-zero energy that e.g. a harmonic oscillator has when it...