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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.


9h
comment Proving that there always exists two opposite points on a circle where the temperature difference is less than 1
You're almost there. You still have to argue that you can't get from $D>1$ to $D<1$ without passing through a point where $|D|\le1$, which is where you'll use the fact that $D$ changes by at most $2$ at a time.
12h
comment Proving that there always exists two opposite points on a circle where the temperature difference is less than 1
Hint 1: Suppose $D > 1$ at some point $i$. What is $D$ at the opposite point $j=i+n/2\bmod n$? Hint 2: How much can $D$ change between adjacent points $i$ and $i+1$?
14h
comment Imaginary Numbers
Previously: What are imaginary numbers?
14h
revised Traveling salesman problem: a worst case scenario
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15h
comment Traveling salesman problem: a worst case scenario
Sorry, no idea.
15h
answered Traveling salesman problem: a worst case scenario
18h
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
+1 Can you find the slope of the lines in log-log space? That would indicate the order of convergence.
1d
answered How to conceptualize unintuitive topology?
1d
comment Exist a function composed by simple continuous functions that $f:\Bbb R \rightarrow \Bbb N$?
Hey look: $\lfloor x\rfloor = x - \frac12 + \frac1\pi \tan^{-1}(\cot(\pi x))$. Can you find the catch?
1d
revised When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
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1d
answered When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
2d
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
If you put "@Rahul" somewhere in your comment I get notified of your reply. It doesn't matter whether the auxiliary function you've constructed is continuous or not. The final integral you compute is ultimately a linear combination of (a) the areas of the Voronoi regions, or (b) the total area of the adjacent triangles of each sample point. With Voronoi, the areas of the Voronoi regions always change continuously if you move the sample points. But with Delaunay, the mesh topology can change, and in that case the result of the integral will change discontinuously upon moving a point.
2d
comment Logic when using two (if/then) statements
By the way, your proposition also implies that someone who does not have the flu automatically passes the course.
Sep
14
comment being $\mathbf{a}$ and $\mathbf{b}$ two vectors with same length, how do I expand $(\mathbf{a}^T\mathbf{b})^2$?
I prefer to write it as $a^Tbb^Ta$, because expressions of the form $a^TMa$ where $M$ is a symmetric matrix are very common. The derivative is $2bb^Ta = 2(a^Tb)b$, which you can obtain from that form or via $\nabla(a^Tb)^2=2(a^Tb)\nabla(a^Tb)=2(a^Tb)b$.
Sep
14
comment Ellipsoidal Decomposition: Finding ellipsoids whose sum contains a given ellipsoid
Are you sure you want the Minkowski sum? Take any cylinder enclosing $E$, and let $X$ and $Y$ correspond to its cross-section and axis respectively. Then the volumes of $X$ and $Y$ are (arbitrarily close to) zero while their Minkowski sum still contains $E$.
Sep
14
revised Evaluating the integral $\int_0^\pi 9\sin^2t\cos^4t\,\mathrm{d}t$
edited title
Sep
14
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
One trivial observation: the Voronoi method is continuous in the sample locations, while the Delaunay method can change discontinuously if the samples are perturbed.
Sep
14
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
If you don't get a good answer here, you might consider asking on scicomp.stackexchange.com.
Sep
14
comment Is the Moment of Intertia of A Thin Rod equal to The Moment of Intertia of a thin Strip?
I imagine a strip as a rectangle with a large length, a small width, and a negligible thickness. Perhaps this is different from what you consider a strip.
Sep
14
comment Is the Moment of Intertia of A Thin Rod equal to The Moment of Intertia of a thin Strip?
You haven't said whether the width of your thin strip is also negligible.