# Recent content by largarithmic

1. ### HSC 2013 MX2 Marathon (archive)

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...
2. ### Cool Things.

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...
3. ### Cool Things.

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...
4. ### Cool problem of the day!

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...
5. ### Nice circle geometry question.

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...
6. ### Is 3/4 a Rational Number

reminds me a bit of this: http://www.tricki.org/article/How_to_solve_linear_equations_in_one_variable
7. ### HSC 2012 MX2 Marathon (archive)

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.
8. ### HSC 2012 MX2 Marathon (archive)

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...
9. ### HSC 2012 MX2 Marathon (archive)

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

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...
11. ### Fundamental Theorem of Algebra.

Random question, would FTA be proved in MATH2962?
12. ### HSC 2012 MX2 Marathon (archive)

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

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...
14. ### HSC 2012 MX2 Marathon (archive)

Re: 2012 HSC MX2 Marathon ^^
15. ### HSC 2012 MX2 Marathon (archive)

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.