Reputation
Top tag
Next privilege 25,000 Rep.
Access to site analytics
Badges
3 38 91
Impact
~549k people reached

Aug
20
comment Trivia question
I'm positive I saw exactly the same question asked on this site not more than a week ago (with the word hendecagon too, no less). In the comments people brought up Bell numbers, but apparently dealing with rotations and reflections makes it problematic. I can't find the old question any more; perhaps it has been deleted?
Aug
20
comment Rotationally distorted cube rectification
Since you haven't told us which ordering of rotations you're using, that's about all I can say at this point.
Aug
20
comment Rotationally distorted cube rectification
The thing about Euler angles is that they are order-dependent, so if I give you a formula that assumes one convention and you're using a different one, it doesn't help you... You can look at Wikipedia's formula for converting a rotation matrix to angles in the $ZXZ$ convention, compare it with the list of rotation matrices for different conventions, and try to adapt the formula for the convention you're using.
Aug
20
comment Is there any way to find the equation for this situation?
Surely the construction looks more like this than the figure in your question?
Aug
20
comment Rotationally distorted cube rectification
Can you get away with just forming a rotation matrix instead of having to recover the Euler angles? If so, the $3\times3$ matrix with $V_x'$, $V_y'$, and $V_z'$ as rows will transform your cube into an axis-aligned one.
Aug
20
comment Why $M=\{(x, |x|), x\in\mathbb{R}\}$ is not an embedded submanifold?
Thanks for improving the question. If you want to show that $M$ is not an embedded submanifold, shouldn't you try to show that there can't be any immersion from $\mathbb R$ into $\mathbb R^2$ whose image is $M$? (What would its derivative be at $(0,0)$?)
Aug
20
comment Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
I've edited the title to be more descriptive. Please check that it accurately reflects the question.
Aug
20
revised Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
edited title
Aug
20
answered Polarity of the Surface Normal of a 3D triangle
Aug
20
comment Similarity between two nPn permutations of the same set.
If you have two permutations $\sigma_1$ and $\sigma_2$, you can find the "difference" between them as the permutation $\sigma_2\sigma_1^{-1}$, of which you can compute the inversion number or the disorder (same thing) as shown by the two existing answers.
Aug
19
comment What is the average length of all integral curves of a vector field?
Your physical motivation is a little tricky, because the average length only gives you a bound on the average time if the magnitude of velocity is bounded from below.
Aug
19
comment Polarity of the Surface Normal of a 3D triangle
What do you mean by the "polarity" of the normal? The cross product $(p_2-p_1)\times(p_3-p_1)$ gives a vector pointing in the direction you want.
Aug
19
comment I want to find out the angle for the expression $a^3 + b^3 = c^3$.
Wookieepedia: The article you requested does not exist.
Aug
19
comment Finding saddle point of a quadratic form
How would you define the saddle point of an inequality-constrained problem?
Aug
19
comment If $x, \log_{10}(x), \log_{10}\log_{10}(x)$ are in arithmetic progression, find the range of $x$.
In case anyone is wondering, the progression turns out to be approximately $1.22802, 0.0892054, -1.04961$.
Aug
18
comment Why is gradient noise better quality than value noise?
"Quality" here mainly refers to the visual aesthetics of the result seen as a texture. You can quantify it a little in terms of the Fourier spectrum (for example, Wikipedia says gradient noise has more energy in higher frequencies), but I think most people just mean "it looks better".
Aug
18
comment How do you pronounce the inverse of the $\in$ relation? How do you say $G\ni x$?
+1, nice reference! I hope it will not be considered rude for me to suggest that you switch the order of "the latter meaning..." and "the former meaning...", which I found confusing at first glance.
Aug
18
comment Uniform distributions on the space of rotations in 3D
Some rationale for scheme #3: The image of the $z$ axis under a random rotation should be uniformly distributed over the unit sphere, so we make that happen. This leaves one degree of freedom in the orientation of the $xy$ plane, so we pick that uniformly as well.
Aug
18
revised Uniform distributions on the space of rotations in 3D
added 24 characters in body
Aug
18
comment The average surface area of a projection of a randomly rotated planar rectangular shape on a two-dimensional surface
I've asked a new question about this to make sure.