Reputation
22,743
Next tag badge:
79/100 score
24/20 answers
Badges
3 36 85
Newest
 Guru
Impact
~409k people reached

Feb
20
comment Are there real solutions to $\exp(X)=-I$?
Hint: $-I$ is also a rotation by $\pi$.
Feb
19
comment Why erf(a-b)+erf(a)+erf(a+b) is so close to 3erf(a)?
This is true for "most" functions, not just $\operatorname{erf}$.
Feb
18
comment A mathematical abstraction of colours?
I don't know what you mean by "one set can't have two distinct parent sets", but you can consider the set of colours generated by additive combinations of (a given set of) colours as a convex cone. Maybe also take a look at how colour models are formalized.
Feb
10
comment Why is a local min also a global min for convex functions?
If $x$ is a local minimum, $f(x)\le f(y)$ for all $y$ in a neighbourhood of $x$. To prove that $x$ is a global minimum, you need to show that $f(x)\le f(z)$ for all possible $z$. Find a $y$ that is on the line segment between $x$ and $z$ and lies in the aforementioned local neighbourhood, then apply convexity.
Feb
10
awarded  Reversal
Feb
9
comment intuitive meaning of sphericity
Intuitively, by "flat space generated by $C$" they mean that if you have (say) a two-dimensional triangle floating in three-dimensional space, you should measure its sphericity by looking only at disks lying in the plane of the triangle, not full three-dimensional balls. (If you did the latter, the asphericity would always be $1$ because there is no 3D ball of positive radius lying entirely inside a triangle.) Further reading: affine hull.
Feb
9
comment Is $4 \times 6$ defined as $4 + 4 + 4 + 4 + 4 + 4$ or $6 + 6 + 6 + 6$?
It doesn't matter. You define $4\times 6$ one way, I define it the other way, we prove multiplication is communicative so our definitions are equivalent, everything is dandy.
Feb
4
revised There is only one interesting measure space
don't use MathJax for text formatting
Feb
2
comment Improvement over gamma correction for brightening images?
You could try $y=x/(a(1-x)+x)$ with $a>0$, which is the one-parameter family of rational functions through $(0,0)$ and $(1,1)$. Related: math.stackexchange.com/q/297768/856
Feb
2
comment Constraint optimization with Calculus of Variations. How to handle positive function constraint?
I don't know. I've only read the textbook by Gelfand and Fomin. It wasn't too forbidding, as I recall.
Jan
31
comment Is it possible to construct a system of equations for which the set of solutions is a plane?
Then mm-aops's second example works: $0x+0y+z=0$. There are $n$ equations in $3$ variables; here $n=1$.
Jan
31
comment In how many ways can we distribute 24 bullets among four burglars?
Are the burglars being armed with these bullets or being shot by them?
Jan
31
comment Decorating eggs
I imagine that a very good empirical solution is already well known, at least for a spherical egg.
Jan
30
comment Constraint optimization with Calculus of Variations. How to handle positive function constraint?
I don't remember the theory, but here's the intuition: If you only enforced nonnegativity at a finite number of points $x_0, x_1, x_2, \ldots$, your Lagrangian would be $L[f] = F[f]-\lambda_0(f(x_0)-0)-\lambda_1(f(x_1)-0)-\lambda_2(f(x_2)-0)-\cdots$ with $\lambda_i\ge0$. But nonnegativity at all points is an infinite number of constraints. So you may consider $\lambda$ a function of $x$, and write the Lagrangian as $$L[f] = F[f]-\int\lambda(x)(f(x)-0)\,\mathrm dx,$$ with $\lambda(x)\ge0$ for all $x$.
Jan
26
comment Physical meaning of some identity in a weighted undirected graph
How did you come across this equation? Some context might help for finding a meaningful interpretation.
Jan
25
comment The top 1% own 50% of the world's wealth - how do we turn this into a function?
en.wikipedia.org/wiki/Pareto_principle
Jan
24
comment Generating Symmetric Matrix
Any such matrix is of the form $A=Q\Lambda Q^T$ with orthogonal $Q$ and diagonal $\Lambda$, such that the minimum diagonal entry of $\Lambda$ has multiplicity at least $2$. Generate such a $Q$ and $\Lambda$ randomly and you're set.
Jan
23
comment Infinite connected graph such that every vertex has finite degree
Sounds about right. Pick a vertex $v$ and consider the number of vertices that can be reached from $v$ in up to $n$ steps. (I assume a connected infinite graph is one in which any two vertices have a path of finite length between them.)
Jan
23
comment How to Distribute Points in a Poisson Distribution in a Circle
Do you mean a Poisson-disk distribution?
Jan
23
comment Confusion about order of operations with point-in-tetrahedron formula
Here's the easy way to test if a point is in a tetrahedron: steve.hollasch.net/cgindex/geometry/ptintet.html