Luboš Motl
Reputation
5,437
Next privilege 10,000 Rep.
Access moderator tools
 Jun 14 comment Maximum number of mutually orthogonal latin square pairs (definition provided) I may have misunderstood what it means for "all pairs to be distinct". I thought it meant that $x_{ij}\neq y_{ij}$ for all choices of $ij$. If it means something completely different, like that the same doublet $(x_{ij},y_{ij})$ can't occur for two choices of $ij$, then of course my comment is totally irrelevant. Jun 14 answered Maximum number of mutually orthogonal latin square pairs (definition provided) Jun 13 comment Prove that the product of a rational and irrational number is irrational It's surely not quite correct. For example, you missed factors of $1/z$ and $1/b$ in evaluating or "simplifying" $xy/z=a/b$. Otherwise the logic is OK. Jun 12 awarded Nice Answer Jun 12 answered How do I combine multiple sets of ratios in order to meet an overall “target” ratio? (word problem supplied to illustrate) Jun 12 answered K3 surface criteria Jun 12 comment Is there an analogue to the “Delta” symbol for ratios? Dear Theo, what I mean by "discontinuous" is that there is no continuous $f(x)$ such that $f(0)$ is positive and $f(1)$ is negative so that $f(k)/f(0)$ which is $\Delta^\times x$ at some moment would be well-defined for all $k$ between $0$ and $1$. That's a warning sign - if one uses $\Delta^\times$ for things that change sign, it could be an unnatural thing that can go awry at moment... I know that $\Delta$ is the Greek counterpart of $D$ but I think it's a good idea to distinguish them. Did your $D$ mean $\Delta$? Jun 11 comment Is there an analogue to the “Delta” symbol for ratios? Dear Theo, $\log(-1)=\pi i$ and $\exp(\pi i)=-1$: is there any problem with that? Something's changing multiplicatively but changing sign would be a discontinuous process in the real numbers, anyway, so it only makes good sense in the complex realm. Concerning the notation, not sure whether I understand which $D$ you mean. Jun 11 revised Is there an analogue to the “Delta” symbol for ratios? added 176 characters in body Jun 11 comment Intersection of two vectors using perpedicular dot product This is really badly readable. Would it be difficult to translate the obscure object-oriented code into normal mathematical language? Jun 11 answered Is there an analogue to the “Delta” symbol for ratios? Jun 11 comment Combinatorial proof that binomial coefficients are given by alternating sums of squares? OK, sorry, I probably don't know what a combinatorial proof is. If that's pictures, I was taught that the most beautiful picture is an equation. ;-) Jun 11 answered Combinatorial proof that binomial coefficients are given by alternating sums of squares? Jun 11 revised Question about Holomorphic functions added 159 characters in body; added 780 characters in body Jun 11 comment Question about Holomorphic functions Pleasure. Maths is trivial - once it's proved. ;-) Jun 11 answered Question about Holomorphic functions Jun 10 comment p chance of winning tennis point -> what f(p) chance of winning game? Thanks for the great edits, @Chris! You're a co-author. ;-) That's exactly what I saw in Mathematica. Jun 10 revised p chance of winning tennis point -> what f(p) chance of winning game? added 352 characters in body Jun 10 answered p chance of winning tennis point -> what f(p) chance of winning game? Jun 10 answered Integral of $\sqrt{1+\tan^2x}$