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3h
comment Rational solutions to $a+b+c=abc=6$
The prime factorizations of the two "larger" solutions are $$\left(\frac{5^2}{3\cdot7},6\cdot\frac{3^2}{5\cdot7},\frac{7^2}{3\cdot5}\right)‌​$$ and $$\left(-2\cdot\frac{4^2}{17\cdot19},-\frac{19^2}{4\cdot17},3\cdot\frac{17^2}{4 \cdot19}\right)\;,$$ so one could try to look for solutions of the form $$\left(s\cdot\frac{x^2}{yz},t\cdot\frac{z^2}{xy},\frac6{st}\cdot\frac{y^2}{xz} \right)\;,$$ possibly with $z=y+2$ and/or $y$ and $z$ prime.
4h
comment Rational solutions to $a+b+c=abc=6$
The "next-smallest" solution is $(-32/323,-361/68,867/76)$.
9h
comment Rational solutions to $a+b+c=abc=6$
One more "small" solution is $(-1/2,-3/2,8)$. For all other solutions, for at least one of $a$, $b$, $c$ the sum of the absolute values of numerator and denominator is at least $200$. Here's the code I used to check that.
10h
comment Stars and Bars vs PIE
@Amad27: There seems to be a widespread misconception that there is something like right and wrong about what should be considered as different / distinguishable. There isn't; you first have to define what the "different ways" that you want to count are, before you count them. Depending on what you're interested in, the order in which you give the presents to the children may or may not matter. Note that for probabilities it's an entirely different question, which is not about arbitrary definitions of distinguishability but about justifiable applications of the principle of indifference.
1d
comment quantum mechanics violate Bell's inequality
@Raja: Of course I can, but I won't. I proved that it's $1$. If you disagree, you should provide an argument. I'm not going to be responding here anymore unless you provide arguments for your claims.
1d
comment quantum mechanics violate Bell's inequality
If you think the ranges make a difference, please provide an argument for that.
1d
comment quantum mechanics violate Bell's inequality
@Raja: You're just repeating stuff you wrote in the question. matlab told you it's $1$. Batominovski told you it's $1$. I'm telling you it's $1$. If you still insist it's $2\sqrt2$, then I'm not sure why you came here to ask a question.
1d
comment quantum mechanics violate Bell's inequality
@Raja: Perhaps that was a misunderstanding. I was asking whether the ranges you specified for the angles affect the validity of my answer. Do you think my answer isn't valid for those ranges? I believe it is.
1d
comment quantum mechanics violate Bell's inequality
@Raja: Does that somehow affect the validity of this answer?
1d
comment Fast multipole method: help on tutorial
Your point about some other student being interested in the tutorial is a good one, but you can also turn it the other way: If someone else has questions about this tutorial they're not going to be exactly the same set of questions as you have; they may have one or two questions that you had, and some others that you didn't have. Then they shouldn't have to wade through all your questions and all the answers to them to pick out the answers to their questions.
1d
comment Fast multipole method: help on tutorial
@laurentpincemaille: That's very kind, thank you, it didn't exactly hurt me :-) I just think that when a question is changed so significantly, without indicating that it was changed significantly, it makes the answer look bad, as if the respondent hadn't addressed most of the question. That's why I wouldn't do that. Another reason is that very few people are going to read through, let alone answer, such a long question with so many subpoints. images and a link to a paper one needs to understand.
1d
comment Stars and Bars vs PIE
@Amad27: There are $\binom{6+k-1}{k-1}$ ways to distribute $6$ equivalent gifts to $k$ children, so $\binom82=28$, $\binom71=7$ and $\binom60=1$ ways to distribute them to $3$, $2$ and $1$ children, respectively. So inclusion-exclusion gives $28-3\cdot7+3\cdot1=10$, in agreement with your first, direct approach.
1d
comment Fast multipole method: help on tutorial
No, I don't, and I think it's bad style to add questions to a question like that after it's been answered. You could ask a new question.
1d
comment Game on simple finite graphs
I added an answer which I believe explains the results for large path graphs (and sketches a proof).
1d
comment Game on simple finite graphs
I added an answer which I believe explains the results for large path graphs (and sketches a proof).
1d
comment Question on occurrences of prime gaps
One cannot use (these sorts of) probabilistic arguments to "show" something about the primes -- only to form expectations and conjectures. There is a priori no reason why the prime gaps shouldn't be far above $\log x$ less often and not so far below $\log x$ more often.
1d
comment Question on occurrences of prime gaps
How are you defining these "numbers of times"?
1d
comment Game Theory: Variants of the Stag Hunt
Are you aware that the problem you've scanned and pasted here builds on another problem and cannot be understood on its own? In particular, the role of the "hare" remains unclear.
2d
comment Why does the surface area of the hypersphere go to zero as the number of dimensions goes to infinity?
That's sort of not very helpful, posting nothing but the link contained in the question as an answer.
2d
comment Why does the surface area of the hypersphere go to zero as the number of dimensions goes to infinity?
If I understand that remark correctly, you seem to have a wrong idea of what "surface area of the hypersphere" means. It refers to a "hyper-area", e.g. the "surface area" of a sphere in four dimensions is a three-dimensional volume.