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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.


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
31
awarded  Necromancer
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 $42$.
Mar
29
comment Why multiply first?
@MJD: Horner's method alternates addition and multiplication, so wouldn't it require the same number of parentheses either way?
Mar
29
comment What is the difference between homomorphism and isomorphism?
"a homomorphism... means that G and H are algebraically identical." No it doesn't. Would you say that $(\mathbb Z,+)$ and $(\mathbb R,+)$ are algebraically identical? And that they are both identical to the trivial group? Only if you have an isomorphism are two algebraic structures identical.
Mar
29
revised Simple & Intuitive Statements that are Difficult to Prove
added source
Mar
28
comment What extra assumption makes this transformation affine?
@joshphysics: I have no idea. As I said, I haven't looked at the proof closely enough to see how well it generalizes.
Mar
28
comment What extra assumption makes this transformation affine?
Also, @BISHD Linearity is obviously a stronger condition than affineness!
Mar
28
comment What extra assumption makes this transformation affine?
Let $y=0$ and you get $f(x+a)-f(a)=f(x)-f(0)$. Define $g(x)=f(x)-f(0)$ and you have $g(x+a)=g(x)+g(a)$. So $g$ is additive, and you want to show that it is linear. I would expect that continuity should be sufficient, though I haven't checked that the same proof goes through.
Mar
28
comment Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
You know Math.pow(2, 42) exists, right?
Mar
27
comment A sufficient condition for a convex body to lie completely inside another convex body?
Just replace the triangle with a thin prism and the point with a tiny sphere.
Mar
27
comment A sufficient condition for a convex body to lie completely inside another convex body?
No. Let $B_1$ be the triangle with vertices $(1,0,0)$, $(0,1,0)$, $(0,0,1)$ and let $B_2 = \{(0.4,0.4,0.4)\}$.
Mar
27
comment Can a piece of A4 paper be folded so that it's thick enough to reach the moon?
Here's a brief explanation of Gallivan's theorem with a nice diagram.
Mar
27
revised Variation on circular lake problem
deleted 14 characters in body
Mar
27
comment Does there exist a polynomial function for every n points, whose extremas are these points?
@Wrzlprmft is right. You should have $n$ equations for derivatives and $n$ equations for values. So use a degree $2n-1$ polynomial. In your example, you'll get $f(x)=-\frac{9}{128}x^5+\frac{31}{64}x^4-\frac{19}{32}x^3-\frac{11}{16}x^2+4$: i.stack.imgur.com/qWEBd.png
Mar
27
comment Can 3 random variables have pairwise correlation -1?
So, by @mookid's answer we see that the pairwise correlations $(r_{XY},r_{YZ},r_{XZ})$ cannot be $(-1,-1,-1)$, while obvious they can be $(1,1,1)$ if $X=Y=Z$. I think the generalized question is interesting: What is the space of possible values of the triple $(r_{XY},r_{YZ},r_{XZ})$?
Mar
26
comment multiplying Gaussian distributions of different dimensions
Can't you just extend the 3-dimensional precision matrix to $n$ dimensions by inserting zeros into the other coordinates? Of course, then it no longer represents a distribution, but it's still a likelihood function. In particular, it's one that is independent of the other coordinates, which is what you want. And for the mean, you don't know anything about the new coordinates, but you can put any value you want into them -- it doesn't matter because $\Lambda\mu$ will zero them out anyway.
Mar
26
comment clockwise or counter clockwise in 3D
You could check the sign of the dot product between $c_1$ and $c_2$, which is positive when the angle is between 0 and 90, and negative when the angle is between 90 and 180.