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seen Oct 15 at 3:07

Oct
6
awarded  Nice Answer
Jul
5
awarded  Yearling
Jul
1
comment Question about Riemann Mapping theorem
It means that if $f,g$ are any two mappings with $f(z_0)=g(z_0)=0$ and positive real $f'(z_0)$ and $g'(z_0)$ (a priori completely unrelated), then $f=g$ everywhere (so $f'=g'$ as well, etc.). As a side note, it would be nice to have some language ministry (or whatever it is called in your part of the world) to establish some canonical way of spelling "Riemann" for its constituents so that the poor outsiders would not have to guess if Reimann and Remiann is the same person or not ;)
Jun
16
comment Irreducibility of $x^n-x-1$ over $\mathbb Q$
This is outlandishly clever! Make sure it gets included into some textbook or lecture notes :-)
Jun
16
comment Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$
What you had in your head when writing this was impeccable. What you wrote in the last few lines is total gibberish.
Jun
15
comment Solving $a^2+b^2\equiv 0$ mod $c$ for distinct integers $a,b,c$ constrained between two consecutive squares
$\frac{x^2+y^2}{c}<\frac{2\cdot(2n)^2}{n^2}=8$
Jun
15
comment Solving $a^2+b^2\equiv 0$ mod $c$ for distinct integers $a,b,c$ constrained between two consecutive squares
Hmmm... I have the desire that is exactly opposite to yours: can you tell how you used a computer here?
Jun
15
answered Solving $a^2+b^2\equiv 0$ mod $c$ for distinct integers $a,b,c$ constrained between two consecutive squares
Jun
15
comment hand evaluate $\sqrt{e}$
"but the fifth term alone involves 11! which is ten multiplications" And if you write a recursive subroutine for it, the cost of the storage of the program state word at every single call will dwarf all the arithmetic together. However, all it means is that not everything should be done in the most stupid way available ;) This is not to say that I do not admire continued fractions, on the contrary. So, for this particular case I voted for your approach, but if $1/2$ were $4/7$, say...
Jun
13
comment How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
True, of course, but it seems pretty clear that the typeset letter combination "integers" should be read and pronounced "reals" in that particular sentence :-)
May
31
comment Chinese estimate for $\pi$. Were they lucky?
@David H Because I understand why Archimedes stopped at $k=4$, but not why Chongzhi stopped at $k=12$...
May
31
comment Uniform continuity proof verification
--I have no idea what I just wrote.-- What exactly do you mean by this????
May
31
comment Chinese estimate for $\pi$. Were they lucky?
@David H Erm... I'm speechless :-)
May
31
comment Chinese estimate for $\pi$. Were they lucky?
Archimedes lived in 200's BC. According to en.wikipedia.org/wiki/Mil%C3%BC, 355/113 appeared about 650 years later!
May
27
comment Number of simple edge-disjoint paths needed to cover a planar graph
Have you tried to look at a necklace of squares in which each square (4-cycle) is connected to its 2 neighbors by edges going out from 2 opposite vertices?
May
27
comment Prove the solutions of following equation exists
Sums of two squares are closed under mutiplication.
May
23
answered Prime Number Theorem and sum of reciprocals of primes
May
23
comment Is a proof still valid if only the writer understands it?
@SpamIAm Come on, a huge carnivorous mammal in your head is hardly better than a nude body, especially if it is capable of thinking that "it is not uncommon in math..." :-).
May
21
answered A property of exponential of operators
May
21
comment Interesting but short math papers?
"A direct search on the CDC 6600 yielded". Note that the year was 1966, so to properly appreciate it, one has to recall the timeline of the computer development. Fortunately, it is just one click away: computerhistory.org/timeline/?year=1964 (I linked directly to the year relevant to the passage in the article but looking at a few adjacent years will certainly give you a better picture of what these words really meant when they were published).