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 Mar 20 comment Unable to reproduce this figure Not Alpha, here try it online Mar 20 comment Unable to reproduce this figure I tried the formula with Wolfram and it looks pretty similar, so it is correct. Not a Matlab expert, but probably you need some more precision with contour plot, as I had problems with it also. Or just specify explicitly what contour levels to plot, try $1/e^{10}, 1/e^{20}, 1/e^{30}, \dots$. Nov 7 comment What are some examples of notation that really improved mathematics? @NateEldredge I think it is an improvement. Compare vector expressed as a series in usual notation $\sum \langle x,\phi \rangle \phi$ and in bra-ket notation $\sum \langle \phi | x \rangle |\phi\rangle$. The bra-ket notation also can be read not just as sum of vectors with coefficients but also as matrix-vector multiplication just by swapping things around. Also we can treat $\sum |\phi\rangle\langle\phi |$ as an identity and it gives rise to a bunch of useful algebraic manipulations. Nov 7 comment What are some examples of notation that really improved mathematics? Einstein's notation is indeed the power of math at its finest! I would add Kronecker and Levi-Civita symbols to this answer. Nov 7 comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? @kriss Thx, next to last was wrong indeed (also the second one), counting to five is hard! Fixed it and also colored the pens for more clearity. Nov 2 comment When written in decimal notation, every square number has at most 1000 digits that are not 0 or 1. True or false? [silly]$2^2 = 3.9999999...$ have clearly more than 1000 nines, so it's false[/silly] Jan 11 comment Minimum number of steps needed to solve a rubik cube It's not the one I'm looking for. This solution I can easily find everywhere, it's more than just 3 steps. Jan 9 comment Minimum number of steps needed to solve a rubik cube @RossMillikan I did solve it with those moves many times, it required some thought to it and I liked it :). Jan 7 comment Minimum number of steps needed to solve a rubik cube @RahulNarain Probably... If someone will write these moves down it would be great. Dec 25 comment Why is 'abuse of notation' tolerated? Oh I remember how as a freshman I was taking notes on math related lectures and was trying to purify math so that I have no words at all there except titles, names and some minor comments and it should be as compact as possible. Now I can make a 10 page theorem proof in to one page so that I can see a full picture just with one glance, it helps a lot. Dec 15 comment Change of variables in Belousov-Zhabotinsky reaction Well, that's what you do when you nondimensionalize your equations. It's a chemistry, so $x,y,z$ are some concentrations so as $A,B$. Then to nondimensionalize a variable $z$ you replace it with something like $\frac{z}{B}$. Dec 15 comment Change of variables in Belousov-Zhabotinsky reaction Or $z -> \frac{z}{B}$, $t -> \frac{\tau}{B k_5}$, $x -> \frac{k_5 x}{2 k_3 A }$ Dec 15 comment Change of variables in Belousov-Zhabotinsky reaction Well just from looking on the 3rd equation I can say, that $z$ was changed to $\frac{z}{k_5 B}$, $t$ to $\frac{\tau}{B k_5}$ and $x$ to $\frac{x}{2 A k_3}$. The rest is easy to do. Dec 15 comment Change of variables in Belousov-Zhabotinsky reaction It can be used for further simplification of the system , to get rid if some equations. But I just realized that it's not the question. Do you just need to know what replacements were used? Dec 15 comment Change of variables in Belousov-Zhabotinsky reaction Take a look at Tikhonov's theorem Oct 1 comment using numbers 1 to 9 only once to equal 1 million @Joren If the question didn't say anything about 'one million' and just stayed that the answer should be 1000000 then it works :)