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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.
Aug
12
answered The puzzle of billiard geometry
Aug
12
comment Do matrices have a “to the power of” operator?
@paul23 fair enough. Exponents like these are normally only defined for square matrices for that very reason.
Aug
12
comment Do matrices have a “to the power of” operator?
can I ask why you were convinced that there were different operators involved in that first expression? There's only one kind of matrix multiplication.
Aug
5
comment How to Garner Mathematical Intuition
@BrianM.Scott part of my point is that your average high-school math student probably wouldn't say that much of it was obvious at all. Or at least that it only seemed obvious in retrospect, once it was clearly stated. You're clearly beyond the point where it could tell you anything new. Are you saying that typical gradeschool math students would also find the book obvious/useless?
Aug
4
comment How to Garner Mathematical Intuition
Saying this isn't well defined seems odd to me. How you go about finding proofs is also a personal matter, but no one has a problem with Polya. It's absurd to say that there aren't general guidelines and ways to think about problems that lead to better intuition. This is vitally important for math education; dismissing the idea of teaching it because it isn't well-defined is precisely the problem in the first place. Can we take a more productive approach?
Aug
3
comment I can't get satisfied with such 'so on' type logic. Is there a better way to solve it?
It is rigorous though, at least with a couple extra steps. All you have to do is show there will always be another point available to choose. Or you might be a finitist, in which case may god have mercy on your soul ;)
Aug
2
answered Guess the functional form of a graph
Aug
2
comment Areas of math that can be “gamified”?
I'm familiar with material on game design; I spent a lot of time on it in highschool and it is my real priority. A lot of my ideas in the direction of "uncover things they're intrigued about" (robotics, biology, crowd dynamics, Escher, music, fractals, social choice, etc.) would probably be used for a presentation or project instead. While I 100% agree with the perspective you're describing, my issue is mainly about finding which areas games are ideal for. I consider 'game Euclid' superior to 'presentation Euclid', and am looking for other examples in this vein.
Aug
2
asked Areas of math that can be “gamified”?