Robert Mastragostino
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 Oct 23 comment Why do we consider tangent spaces and what not, when we can just use Whiteney's Embedding Theorem and do calculus in $\mathbb{R^{2m}}$? While I suppose this is more a personal preference, working with things like tangent vector fields in $\mathbb{R}^3$ and lugging dot products etc. everywhere is more tiresome than working with an intrinsic metric. I'd imagine that situation only gets worse in the general case. Oct 3 comment Riddle: 1 question to know if the number is 1, 2 or 3 @JohnP couldn't it be easily altered? I.e. "Is the sum of your number and a number uniformly chosen from $\{0,1\}$ greater than 2?" Sep 21 awarded Nice Question Sep 10 comment mathematics behind the derivation of Lorentz transformations @Galoisfan I said that it preserves vector operations. These are precisely the linear transformations. I suppose if you interpret 'vector operations' in a freer way then you can include affine transformations, but the question asks about the Lorentz group and not the Poincare group, so I left this out. Affine maps are simply linear map+translation anyway, so that's trivial. Sep 9 answered mathematics behind the derivation of Lorentz transformations Sep 6 comment Where to start? 1. What level of math have you formally studied, whether or not you feel you remember it? 2. You clearly have no issues forgetting how to add, I assume. What's the earliest point that you have trouble remembering properly? Aug 29 comment Recommended math background for game theory In "pure mathematics"? Like what? Formal logic and set theory are hardly necessary. Aug 29 comment The use for solving quadradic equations for high school students What most students don't realize is that quadratics could really be substituted with something else in the same way that Hamlet could be substituted for Macbeth in an English curriculum. It's not the particular material that matters, but the skill developed by doing it. Aug 28 comment Is it possible to alternate the law of mathematics? The idea of "mathematical laws" isn't too clear to begin with. If I come up with a new type of number system I don't call it a new "mathematical law". It just takes a logical place alongside the old ones, without really being considered as part of "another universe's mathematics". Systems with contradictory axioms live happily together in math as alternatives, which is a bit different from the other sciences that cleanly separate "real" from "hypothetical". You might go for a universe that uses number systems differently? e.g. counting isn't done with naturals, but modular arithmetic. Aug 26 answered Teaching a 4 year old maths Aug 21 comment The puzzle of billiard geometry @LukeAllen Both approaches are common on this site, as you would know if you stayed for awhile and observed how the site is used in practice before deciding what is and isn't acceptable behaviour. Your initial two comments were valid, and if you had continued being respectful and detailed your particular confusion I would have had no problem elaborating and potentially providing a solution. The later ones are you just digging your heels in and deliberately refusing to do 5 minutes of clearly directed reading. "GTFO" certainly doesn't label you as someone deserving of assistance. Aug 21 comment The puzzle of billiard geometry @LukeAllen If you were willing to do any work you would have solved it by now. You have side lengths and you want angles. The methods of conversion are covered within the wikipedia page, and at the very beginning of essentially any resource on the subject. It's not like your example at all, because I've given you the specific place to find your information, and you're just refusing to read it. If you get stuck there then ask more, but don't just whine about not being spoon-fed a formula. Aug 20 comment 'Interesting' orthogonal martices? What does the algorithm do? To check for floating point errors I'd use matrices with both very small and very large components arranged so that 1) very small quantities are added to large ones, or 2)small quantities are inverted. Aug 16 comment Geometry and Physics Possibly do an overview of some of the more complicated concepts they might not have come up with on their own? Symplectic geometry, Fiber bundles, and that sort of thing? Do diagrammatic calculi count as geometry? Road to Reality has a good amount of this sort of thing. Aug 15 answered three dimension and maxima and minima Aug 15 comment Do matrices have a “to the power of” operator? @TonyK I've been burned too many times to make assumptions. I normally figure that somewhere, someone has tweaked a definition to apply to some new bizarre case in a way I've never heard of before. You could define it to insert transposes in the appropriate places to make the right-multiplications compatible, for example, though I don't know of anyone actually using such a thing. Aug 15 comment Algorithm of creating dual graph from a plannar graph Keep in mind that the dual depends on the planar embedding. So it's not a property of the graph in abstract; geometry will be necessary. Aug 14 comment Why is $\pi r^2$ the surface of a circle @euclid that's because it's only a hexagon, so half the outer perimeter is only $3$. It gets better if you use more pieces. Going into the complexities of the number $\pi$ itself is probably beyond the question being asked. Aug 13 comment The puzzle of billiard geometry @LukeAllen I'm not hoping for points.;Very few people on this site work that way. If you take 10 minutes to learn the basics of trigonometry any of the very first things you see will be able to give you a direct answer. What I'm not going to do is spoonfeed you. I've given you everything you need to know beyond the formula itself. Aug 13 comment The puzzle of billiard geometry @LukeAllen do you know trigonometry? You now know all 3 side lengths of both triangles. You can figure out the angles using those and trigonometric functions.