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Re: HSC 2013 4U Marathon Can be solved by squaring all sides and doing tricks like changing a \frac{k-1}{k} to \frac{k}{k+1} to make it bigger/smaller as appropriate. Something you mightn't have noticed about the expression in the middle is that it is actually equal to...

Yeah it's really cool! University is going great - I've been taking 2nd/3rd year maths subjects, putting the most time into 3969 and 3966 - I was very much tempted to put down "the Lebesgue integral" as something here as 'cool', but it doesn't have the simplicity of the Euler characteristic (and...

One of my favourite things is the Euler characteristic / Euler's formula; basically for any "nice" polyhedron, if V is the number of vertices, E is the number of edges and F is the number of faces, V - E + F = 2 always. And if you change the space you're working in to something nasty and...

This reminds me of a really neat (but actually pretty hard) problem: Given a polygon, we define a "flip-stick" to be the following process: take a 'cut' of the polygon (i.e. a line segment that cuts the polygon into exactly two new polygons), then take one of the polygons you produced, reflect...

HEY JOHN GUESS WHO You can also do a really neat trick using Ptolemy's theorem (wikipedia it, its neat and elementary, has come up in HSC before): Suppose there exists D, D' distinct on the same arc AC such that AD/CD = AD'/CD', i.e. AD.CD' = AD'.CD . Also ACDD' (or in the other order) is...

reminds me a bit of this: http://www.tricki.org/article/How_to_solve_linear_equations_in_one_variable

Re: 2012 HSC MX2 Marathon I assume the inequality signs are supposed to be the other way; but youve got a problem because there are by no means the same number of summands in sum aiaj and sum aiajak.

Re: 2012 HSC MX2 Marathon It doesnt just depend on whether its a plus or minus though. Like, you have I think n-2 or n-3 sums after that, and its not clear that given a certain sum it has say, a bigger absolute value, than the one that comes after it for instance. Sorry but I just dont buy the...

Re: 2012 HSC MX2 Marathon It's not clear at all why the whole second part thingo after the sum ai is necessarily positive.

Since there's been a mood for cool problems recently, here's one. It's pretty hard but neat ^^ Let S be a (possibly infinite) collection of open intervals such that the union of S covers the closed interval [0,1]. Prove that there is a subset T of S with finitely many elements such that the...

Random question, would FTA be proved in MATH2962?

Re: 2012 HSC MX2 Marathon Uh thats not the riemann hypothesis... Also you're usman, right?

Re: 2012 HSC MX2 Marathon A beautiful question for those who have an idea what modular arithmetic is (basically you reduce every number to its remainder when divided by a number, e.g. 13 becomes 3 modulo 5, 17 becomes 5 modulo 6. Its easy to check that if say A reduces to A', and B reduces to...

Re: 2012 HSC MX2 Marathon ^^

Re: 2012 HSC MX2 Marathon Ah okay; 1st or 2nd sem? and I'm in mon 12 tute for 2962, and not sure about 2961 - any possible tute clashes with either phys chem or chinese lol, but Ill probably be going to the wed 2pm one - gotta work that out in next week, though.

Re: 2012 HSC MX2 Marathon Oh awesome, is that an honours course? I assume btw youre taking 2961/2 this semester?

Re: 2012 HSC MX2 Marathon Im pretty sure eventually you guys will find that stuff like invariance under reflection/transformation is far more useful and fundamental than stuff like integration by subtitution :P euclidean geometry itself is useless; analysis when thought slightly geometry is...

Re: 2012 HSC MX1 Marathon Is that sorta stuff like, allowed/used in 3u, when people dont really even know what converges/diverges mean? Also, sorry man for not talking to you today outside the timetabling unit

Re: 2012 HSC MX2 Marathon You can like, do that integration thing just by considering the geometry of it right; like sending x -> a-x is the same as reflecting the graph about the line x = a/2, so the area under the curve between 0 and a is preserved

oh right yeah, there are many many many solutions (infinite number) as you get closer and closer to the north pole :P