Grigory M
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 Apr 8 comment Proof of the binomial identity $\displaystyle\binom{m}{n}=\sum_{k=0}^{\lfloor n/2 \rfloor} 2^{1-\delta_{k,n-k}} \binom{m/2}{k} \binom{m/2}{n-k}$ Apr 8 comment Proof of the binomial identity $\displaystyle\binom{m}{n}=\sum_{k=0}^{\lfloor n/2 \rfloor} 2^{1-\delta_{k,n-k}} \binom{m/2}{k} \binom{m/2}{n-k}$ that's just a special case of en.wikipedia.org/wiki/Vandermonde%27s_identity Dec 25 comment Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$ coloured squares also can be counted visually: mathoverflow.net/questions/8846/proofs-without-words/8847#8847 Dec 14 comment How does one read $\bar{A}$ aloud in Russian? «A с чертой» is frequently used (have never heard «A с надчеркиванием» in my life) Nov 27 comment Using the Fano plane for octonion multiplication Oct 13 comment Source and/or combinatorial interpretation for $F_{n+k} = \sum_{i=0}^{k} \binom{k}{i}F_{n-i}$ Oct 9 comment Another binomial coefficients sum Oct 3 comment Area of hyperbolic triangle definition @KWSK Well, (hyperbolic) lengths of both the base and the (hyperbolic) perpedicular are manifestly invariant under hyperbolic motions. Oct 3 comment Area of hyperbolic triangle definition Well, one reason is that in hyperbolic geometry $ah_a\neq bh_b$, so this 'area' would depend on the side we choose as the base — so in a sense it's not well-defined. Oct 3 comment Area of a right angled hyperbolic triangle as function of side lengths Is $\tan(S/2)=\tanh(a/2)\tanh(b/2)$ nice enough? Oct 1 comment Combinatorial interpretation of identity: $\sum_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$ (Re: generalization) indeed Oct 1 comment Combinatorial interpretation of identity: $\sum_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$ @Darij, Alexander thank you — I hope I fixed the typos Sep 19 comment A three variable binomial coefficient identity @darij why, I already do (see par. 3 of 'Comments and thoughts' there) Sep 12 comment Is any 2$m$-dimensional manifold almost complex? locally — yes, globally — no Aug 23 comment Is the functional equation for $\zeta (s) \left(1-\frac{1}{3^{s-1}}\right)$ known? Yes, just change $2^{-s}$ to $3^{-s}$ (and $2^{-s-1}$ to $3^{-s-1}$) in the func. equations for $\eta$. Aug 21 comment The form of the zeta function of an elliptic curve over a finite field And of course a proof for $y^2=x^3-x$ goes back to Gauss (see e.g. Ireland, Rosen. A Classical Introduction to Modern Number Theory, ch. 8 for the proof) Aug 21 comment The form of the zeta function of an elliptic curve over a finite field Well, there is a relatively elementary proof in Silverman. The Arithmetic of Elliptic Curves Aug 10 comment Cohomology of $K(\mathbb{Z}_2, n)$ See doc.rero.ch/record/482/files/Clement_these.pdf (including tables in Appendix C). In particular, yes, $H^5(K(Z/2,2))$ has 4-torsion, and no, I don't think there is a really simple and explicit answer. Aug 9 comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta) related: math.stackexchange.com/q/1284161 Aug 9 comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta) the link is dead...