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 Nov 27 comment Is the translation of open and closed sets to some language non-antonym preserving? Interesting, thanks. Apr 16 comment Is this already an equation/law that has been found? I've only seen that attribution in "Die Vermessung der Welt". Apr 1 comment Formal Variational Calculus Reference Request Arnold's book "Mathematical Methods of Classical Mechanics" has something to say about that. You might be also interested in Bleecker's "Gauge theory and variational principles" Jan 27 comment Multivariable Limits Well, it's replacing, say, log(a^z) by $\log(a^z)$, etc. You can edit your own answer correcting that. Take a look at tobi.oetiker.ch/lshort/lshort.pdf Jan 26 comment Multivariable Limits It'S not that hard :). What you wrote here is mainly only missing a pair of $ enclosing the math. Jan 25 comment Multivariable Limits Would you mind writing in TeX format? please? Jan 23 comment Describing the algebra of functions on$S^2$indeed, sorry :), well, it's negative. Have a look at M. Paschkes' Ph.D. thesis., page 43. Browse "paschke" here wwwthep.physik.uni-mainz.de/Publications/theses Jan 22 comment Is length adimensional when space is not flat? Thanks 5PM, my apolgies, I should have written the "(squared) length element$dr^2+r^2dθ^2$has the same units as$dx^2+dy^2$". Jan 14 comment two identical point charges can't collide I agree with Haskell's claim. To clarify, I've been talking only about two inertial frames:$S$, w.r.t which the particles have position$\mathbf q_i$, and$S'$, defined by having the origin at$Q:=(\sum_i m_i \mathbf q_i)/(\sum_i m_i)$. If you write down Newton's second law for$Q$, it's equation of motion is$\ddot{Q}=F_{12}+F_{21}\equiv 0$(by third law), whence$Q(t)=Vt$for some constant vector$V$. If one of them is inertial, both are. Jan 14 comment two identical point charges can't collide @uncookedfalcon Yes, but if you don't like that frame, you can replace$\mathbf{r}$everywhere by$\mathbf q_1-\mathbf q_2$. The same analysis caries over to this "more general" frame. Regarding your question, both frames are inertial (because setting the force to zero, you get a particle that follows a stright line with constant velocity as the solution to the differential equation). Does that answer your question about frames? Jan 13 comment two identical point charges can't collide @uncookedfalcon if you wish to analyze the problem in arbitrary dimension, the field is no longer inverse-square dependent. Jan 13 comment two identical point charges can't collide If your law is to have physical meaning, it must be$n=3$and in Newton+Coulomb law it's not the norm squared, but to the third power. Jan 12 comment Metric tensor of complex numbers & Hamiltonian Mechanics I've found it. It's "Introduction to Mechanics and Symmetry" by Marsden and Ratiu, Exercise 2.1-1. Jan 11 comment Metric tensor of complex numbers & Hamiltonian Mechanics the$2$factor comes from the definition of the partial with respect to$\bar{z}$. // These equations are$N$complex equations, so$2N$real eqs. I think I saw that once on one of Marsden's books. Let me search... Jan 11 comment Metric tensor of complex numbers & Hamiltonian Mechanics Ah, I see. But curvature has double derivatives of the metric tensor. In this case$\eta$is the metric tensor on the nose :) en.wikipedia.org/wiki/Riemann_curvature_tensor Jan 11 comment Metric tensor of complex numbers & Hamiltonian Mechanics @AimForClarity I'm not sure I understand why you write "curvature" for$\eta$. I do not understand that part of the question. Jan 5 comment Earth-Sun distance equation Jan 1 comment 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries Very rich answer indeed! I appreciate specially the reference to Landsman's notes, which I didn't knew. Jan 1 comment Trouble simplifying a tough equation$1=HappY(Ne^\omega)^{-1}Ye^{ar}$to be more accurate. Dec 24 comment Identifying a surface$\rho^2\cos(2\phi)-1=0\$ @Rakisbro I updated...