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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.


Mar
3
comment How to scale a polyhedron contained a 3-sphere?
@lvella, just checking: did it work for you?
Mar
3
comment probability of three random points inside a circle forming a right angle triangle
I'm sure you agree that if the angle of the triangle is $89^\circ$ or $91^\circ$ then it is not a right angle. But you also have to remember that it is also not a right angle if it is $90.1^\circ$, or $90.01^\circ$, or $90.000001^\circ$, and so on. Only when it is $90.000000000\!\ldots^\circ$ is it a right angle. So maybe now you can appreciate why this can only occur with vanishingly small probability.
Mar
3
comment probability of three random points inside a circle forming a right angle triangle
What are your thoughts? What have you tried so far?
Mar
2
comment How should I deal with this two-dimensional $\frac{0}{0}$ limit?
I think you mean $\lvert f_u \rvert$, $\lvert f_v \rvert$ are zero near $(0,0)$.
Mar
1
answered Question about norms of a matrix when exchanging two of its rows
Mar
1
comment Question about norms of a matrix when exchanging two of its rows
I thought (and Wikipedia agrees) that the Euclidean norm of a matrix was the operator norm $\lVert A \rVert_2 = \max_{x\ne0}\lVert Ax\rVert_2/\lVert x\rVert_2$, and that's not an entrywise norm. If Wikipedia is incorrect, someone should correct it. If the term is ambiguous, the asker should clarify which meaning is intended.
Feb
29
comment Logarithms explained simply
Logarithms are to exponents what division is to multiplication. How do you divide 5 by 12, in words?
Feb
28
comment Deriving the Area of a Sector of an Ellipse
I don't think this is correct. In your coordinate system, the line joining the origin to the point $(x,y) = (a\rho\cos\theta, b\rho\sin\theta)$ does not subtend an angle of $\theta$ with the $x$-axis, so your limits of integration won't be the $\theta_1$ and $\theta_2$ given in the figure.
Feb
28
revised Why is boundedness defined so differently in a topological vector space and in a metric space?
Wiki (http://en.wikipedia.org/wiki/Wiki) ≠ Wikipedia
Feb
28
answered Deriving the Area of a Sector of an Ellipse
Feb
28
comment Hard Geometry Problem: Circles
Why is the problem repeated twice in the question?
Feb
27
revised How can I evaluate an expression like $\sin(3\pi/2)$ on a calculator and get an answer in terms of $\pi$?
Latex editing.. Verify if this matches with what you want..
Feb
26
comment Does an identity exist for ALL functions?
"Most" binary functions do not have an identity. A couple of simple explicit examples are the $\min$ and $\max$ functions on the integers or the real numbers. However, $\max$ has an identity on the natural numbers...
Feb
25
comment How to justify small angle approximation for cosine
How about completing the square and ignoring the fourth-order term in $\theta$? $\sqrt{1 - \theta^2} = \sqrt{1 - \theta^2 + \theta^4/4 - \theta^4/4} \approx \sqrt{\big(1 - \theta^2/2\big)^2}$.
Feb
25
revised Why is $\langle x,y \mid x^3=y^2=(xy)^3=e\rangle$ a presentation of $\mathfrak{A}_4$?
improved formatting
Feb
25
comment The square root of a variable is negative?
I'm not restricting the domain at all. The statement that $1 = -1\times-1$ is true in complex numbers and quaternions as well. What I don't understand is that you agreed that $x$ equals $1$ and also equals $-1\times-1$, but objected when I said that $1=-1\times-1$. Do you believe that if $a=b$ and $b=c$ then $a$ may not be equal to $c$?
Feb
24
comment The square root of a variable is negative?
No, if $1 = -1\times-1$ then $\sqrt 1 = \sqrt{-1\times-1}$. That is what it means for two things to be equal: it means they are the same thing.
Feb
24
comment Connectivity in Graphs: removing edges vs. removing vertices
The one-vertex graph is not disconnected. But the rest of your argument looks fine to me. By the way, I think you mean "removing the vertex $x$ or $y$" in your second paragraph.
Feb
24
comment The square root of a variable is negative?
All of those are equal to 1. Going to the quaternions doesn't change anything for this question.
Feb
24
comment Evaluating a line integral of a vector field numerically
I added the image and the equation to your post. How exactly do you have your vector field $F$? Is it a pair of rectangular arrays for the $x$ and $y$ components?