@sarah No no. Think of the Cauchy theorem like this : You are applying force and the corresponding displacement is with you. But you are doing this at infinitesimal level and in a closed curve if you add up the displacements of a point traversing through the path then it's 0 (it comes back to where it started looping).
@Alizter My textbook has questions like "Find the circumcentre of the triangle whose vertices are given by the complex numbers $z_1, z_2, z_3$". Arent these problems better suited to coordinate geometry?
@BalarkaSen hmm. I need to focus on studying well for these two years ahead. Especially cambridge entrance exams. The math questions are so difficult that nobody has ever gotten full marks
@ArthurFischer If you have time, can you have a look here in tagging chatroom? (I am not sure whether my ping from here reached you; since your comment is already deleted.)
I have updated my question with some code: http://math.stackexchange.com/questions/873899/successive-ratios-of-a-sequence-is-this-limit-true It relates the error in approximation of this sequence: http://math.stackexchange.com/questions/870989/number-of-compositions-does-this-sequence-have-a-closed-form to the roots of the equations -x^3 + (y+1)*x^2 + 1 == 0 solving for x.
theres a planet, on which aliens with three arms and some antennas live. one day all of them decided to hold hands so that: $1)$every arm was being held $2)$every alien was holding hands with exactly three other aliens $3)$if two aliens held hands, then one of them had six times less antennas than the other alien. Can the total amount of antennas be $9001$?
I think I need to learn quite a bit of stuff before blogging all over.
Anyway, so , where was I? Ah, yes. @blue.
Consider Spec Z. Consider Spec Z[i]. Latter is "sitting over" the other in the sense that multiplying out conjugate primes gives primes in Z. For example, ideals (2 + i) and (2 - i) are sitting above 5 = (2 + i)(2 - i). Interestingly, for 2, say, one has (1 + i) and (1 - i) but both are the same ideals (multiply out by an appropriate unit).
So this "natural" map Spec Z[i] --> Spec Z looks like a ramified 2-sheeted covering of topological spaces, doesn't it? What am I missing?
Oh hang on a second. Some primes don't cover at all! Yeah, how can I forget them : the ideal (3) just sits there. It's a prime ideal in both Z and Z[i]. Then the fibres over (3) is just itself and nothing else and... that means there is a single cover around that ideal after all... ? Am I making sense?
