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Recent content by largarithmic

  1. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    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. largarithmic

    Fundamental Theorem of Algebra.

    Random question, would FTA be proved in MATH2962?
  12. largarithmic

    HSC 2012 MX2 Marathon (archive)

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

    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. largarithmic

    HSC 2012 MX2 Marathon (archive)

    Re: 2012 HSC MX2 Marathon ^^
  15. largarithmic

    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.
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