22,161 reputation
23384
bio website
location
age 30
visits member for 4 years, 6 months
seen 3 hours ago

23h
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 $n=1$.
1d
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?
1d
comment Decorating eggs
I imagine that a very good empirical solution is already well known, at least for a spherical egg.
1d
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
28
comment Under which branch of mathematics do vectors fall into?
See analytic geometry and linear algebra.
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
Jan
22
revised What does $H X H^T$ do?
added 80 characters in body
Jan
22
comment Why can a circle be described by an equation but not by a function?
The standard definition of the square root function is that it evaluates to the positive square root.
Jan
22
comment Basic Differential geometry: Shortest path between two points in R^3 is straight.
Have you tried computing $f'(t)$? What have you got so far?
Jan
21
answered What does $H X H^T$ do?
Jan
20
comment L0 norm, L1 norm and L2 norm
None. You can multiply $y$ by any nonzero scalar and it doesn't change the $L^0$ norm.
Jan
20
comment Optimal size of n circles to fit an area given their relative sizes
Even if all the sizes are equal, this is a pretty tricky problem and no general solution is known: en.wikipedia.org/wiki/Circle_packing_in_a_square
Jan
20
comment Why do transcendental numbers exist?
For your revised question: There are only a countable number of finite sequences of operations.
Jan
20
comment Solutions to $1 - \frac{r'^2}{2c^2} + \frac{r r''}{c^2}=0$?
$1/r^2$ is never zero, so the equation is equivalent to $1-r'^2/2c^2+rr''/c^2=0$, isn't it?
Jan
20
comment What is the exact and precise definition of an ANGLE?
First of all, you haven't actually defined $f$. Is it any function from "corners" to reals? Can I choose $f(abc)=42$ for all $abc$? Second of all, any definition you gave in this framework could not distinguish positive and negative angles, or give a meaning to angles greater than $\pi$, because you've defined a corner just as a set $A\cup B$ with no notion of orientation. So this does not address the confusion expressed in the OP's question.