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Almost all of the questions on the front page these days are homework questions or textbook exercises. I think I'll be spending a lot less time here.

I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


21h
comment Find normal vector for the surface F(x,y)=0
A "surface" $f(x,y)=0$ in two dimensions is usually called a curve.
21h
comment Why is $sinx$ the imaginary part of $e^{ix}$?
Your question is "Why is $e^{ix} = \cos x+i\sin x$?" Hans's linked question is "How to prove that $e^{it} = \cos t+i\sin t$?" I don't see how you fail to see at least a passing resemblance.
1d
comment On Polar Decomposition [Unusual]
Hint: Use the SVD of $F$.
2d
comment Covariance matrix with constant diagonal
It's a multiple of a correlation matrix.
2d
comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
Interesting; I didn't know \big< gave you \langle.
Apr
12
comment A variation of the isoperimetric problem in the plane
@Sébastien: Yes, I agree that there might be an self-intersection problem with non-convex polygons. I'm not entirely convinced by your example, but the problem probably does arise with this Pac-Man-like shape: $n$ points $A_1,\ldots,A_n$ with $A_i = \bigl(\cos(2\pi i/n), \sin(2\pi i/n)\bigr)$ for $i=1,\ldots,n-1$ and $A_n = (-1+\epsilon,0)$. Oh well. I intend to rigorously clarify the limits of my answer in the future, but I may not have time in the next three days.
Apr
11
comment Visually deceptive “proofs” which are mathematically wrong
@Cole: Because I wrote my original comment before that answer was posted. And I'm not so quixotic as to go around complaining about every single answer I don't like.
Apr
11
comment Visually deceptive “proofs” which are mathematically wrong
@Cole, David: I still disagree; the deceptiveness of this argument is not inherently visual. For example, you can tell it to someone over the phone, which you can't do with most of the other fallacious "proofs" on this page.
Apr
9
comment Visually deceptive “proofs” which are mathematically wrong
Is this a visually deceptive "proof"?
Apr
9
comment Symbol for $\left\{ x \in \mathbb{R} : x > 0 \right\}$
Duplicate of How does one denote the set of all positive real numbers? Apropos of most of the answers, see also Does set $\mathbb R^+$ include zero?
Apr
8
comment Do All Structures have a lower dimensional analogy?
Here's an example you might enjoy: The generalization of a regular polygon is a convex regular polytope. In 2D there are infinitely many, in 3D there are five, in 4D there are six, and in higher dimensions there are always only three (the generalizations of the tetrahedron, the cube, and the octahedron). And of course in 1D there is only one: the line segment.
Apr
8
comment Finding the curve length
$x$ and $y$ are just labels. If you know how to solve for the curve length when $y = f(x)$ in the $xy$-plane, then you know how to solve for the curve length when $q = g(p)$ in the $pq$-plane, or when $א = ш(क)$ in the $אक$-plane. So maybe you can solve for the length of the curve $x = f(y)$ in the $yx$-plane.
Apr
8
comment A variation of the isoperimetric problem in the plane
I'll add some diagrams to this answer later if I find some free time.
Apr
8
comment Visually stunning math concepts which are easy to explain
"Visually stunning math concepts which are easy to explain"
Apr
7
comment Why the $\log$ is so special?
Bitcoin prices on a log scale: bitcoincharts.com/charts/mtgoxUSD#tgMzm1g10zm2g25zl
Apr
7
comment It would be possible to use the covariance matrix $C'=XX^T$ instead of the standard $C=X^TX$ to get the same result on PCA?
If PCA is what you want, you should consider just taking the SVD of the original matrix $X$ instead.
Apr
6
comment 5th order Polynomial not accurate enough?
Can you post a picture of the plot? I think you might be suffering from overfitting and Runge's phenomenon.
Apr
4
comment A function $F:\mathbb{Q} \rightarrow \rm numerators$
Yet another casualty of the difference between the mathematical definition of function (a certain kind of subset of a Cartesian product) and the naive intuitive interpretation of function (a specified sequence of arithmetic operations).
Mar
30
comment Why is there a different button for 'minus' and 'negative' on a calculator?
@Dan: No, I have an infix-notation calculator. 42- is incomplete input in infix notation; only once you enter, say, 42-3= do you get a result 39. How would you get from $42$ to $-42$ in your infix-notation calculator without a negation button?
Mar
29
comment Why is there a different button for 'minus' and 'negative' on a calculator?
Suppose I have the number $42$ displayed on my calculator. I want to negate it and get $-42$, but my calculator does not have a "negative" button. I try pressing the "minus" button, but I don't get $-42$; instead my calculator sits there and waits for me to enter another number to subtract from $42$.