19,072 reputation
23070
bio website
location
age 29
visits member for 3 years, 8 months
seen 2 hours ago

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.


Mar
8
comment Simplifying the expression $\sqrt{(1+\cos t)^2+(-\sin t)^2}$
Strictly speaking that should be $2\lvert\cos t/2\rvert$. For the limits in the question it doesn't make a difference, but in general it does.
Mar
7
comment Natural uses for the co-product of sets?
I think MJD's point was precisely that humans don't come equipped with a tag.
Mar
7
comment Best closed convex surface fitting N points in 3D
The problem of reconstructing surfaces from scattered point sets is well studied in computer graphics. You could try the Eigencrust algorithm which is quite resistant to outliers.
Mar
6
comment Given two non-isomorphic graphs with the same number of edges, vertices and degree, what is the most efficient way of proving they are not isomorphic?
In general, it is not known whether graph isomorphism can be checked efficiently. In this case, however, the first graph is $K_8$ with two disjoint squares $ACHF$ and $BDGE$ removed; the second graph is $K_8$ with an 8-cycle $AFEBHCDG$ removed. So the two are not isomorphic.
Mar
6
comment Infinite series of tangential circles?
$A$ and $B$ are required not to be tangent to each other in the original question. That's not too hard to arrange, but inverting parallel lines will not do.
Mar
5
comment Why is this a quadratic programming problem?
Probably easier to do $\|\mathbf i_k-\mathbf M_k\mathbf a\|^2 = (\mathbf i_k-\mathbf M_k\mathbf a)^\intercal(\mathbf i_k-\mathbf M_k\mathbf a) = \mathbf i_k^\intercal\mathbf i_k - 2\mathbf i_k^\intercal\mathbf M_k\mathbf a+\mathbf a^\intercal\mathbf M_k^\intercal\mathbf M_k\mathbf a$, from where you can immediately see a constant term (which can be ignored), a linear term, and a quadratic term.
Mar
5
comment Why is this a quadratic programming problem?
Are $I_k$, $M_k$, $A$ scalars, vectors, matrices, ...?
Mar
4
comment Estimating powers like $1,000,000^{0.000001}$
This doesn't seem to be a question.
Mar
4
comment Find tangent vector to surface given a point on the surface and its normal vector (for a sphere)
If by "oriented the same way" you mean what I think you mean -- is it possible to choose a unit tangent vector at every point on a sphere such that the field is continuous? -- then no, there is no way to do so.
Mar
3
comment Strangest Notation?
"A woman stepped forward and asked, / What is the strangest day? // Tuesday, the Master replied." —Kehlog Albran, The Profit
Mar
3
awarded  Good Answer
Mar
3
comment How to get a vector field from its rotation field?
Whoa. Where does this come from? Do you have a proof or a reference?
Mar
3
revised Does this series $2 + 4 + \cdots + \sqrt{\sqrt{n}} + \sqrt{n} + n$ have a general term?
Edited title to match body
Mar
3
comment linear line-line intersect **without endpoints**
In 2D, unless the vectors are parallel, the two lines will always intersect. Are you asking how to check whether two vectors are parallel?
Mar
2
comment For arbitrary vector, $v \frac{dv}{dt} = \vec{v} \cdot \vec{ \frac{dv}{dt} }$?
$\mathrm dv/\mathrm dt\ne\sqrt{a'^+b'^2}$. What you have there is $|\mathrm d\vec v/\mathrm dt|$.
Feb
28
comment Can you make the circle into a vector space?
@Sammy: Who said anything about order?
Feb
28
comment Can you make the circle into a vector space?
Trivial solution: Let $f$ be a bijection from the circle to the real line. Define addition and scalar multiplication on the circle via $x+y=f^{-1}\big(f(x)+f(y)\big)$, $ax = f^{-1}\big(af(x)\big)$. Done.
Feb
28
comment A puzzle that came when I am half awake
This is essentially just a restatement of the problem.
Feb
27
comment How to evaluate the curvature by using normal gradient of a function?
Glad it helped! If you find the complete solution, feel free to post it as an answer to your own question for the benefit of other readers.
Feb
27
comment How to evaluate the curvature by using normal gradient of a function?
Have you tried expanding out the definition $\kappa = \nabla\cdot(\nabla\phi/|\nabla\phi|)$? Where did you get stuck? Try using the fact that $\nabla\cdot(\psi\vec A)=\vec A\cdot\nabla\psi + \psi\nabla\cdot\vec A$ where $\psi = 1/|\nabla\phi|$ and $\vec A=\nabla\phi$.