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Nov
12
comment Smallest circle enclosing three disjoint circles
This is known as Apollonius's problem. The Wikipedia article lists a lot of different solution methods.
Nov
12
comment Can I assign a gravity field to an infinite grid of point masses?
+1: Computing the potential first is a good idea. If you add a constant to each potential contribution so it assigns say $(\frac12,\frac12)$ a potential of zero, it looks like the sum doesn't diverge: i.stack.imgur.com/m7Vu4.png (this is with point masses at $\{-100,99,\ldots,100,101\}^2$ and a $-1/r$ potential). I haven't proved absolute convergence though.
Nov
12
comment What is fleventy five?
Fleventy-five will be standard usage in the year 207̃012
Nov
11
comment Why using Gradient Descent?
If you want to minimize $f(x)=x^6/6-x^2/2+x$ by setting the derivative to zero, you have to solve $x^5-x+1=0$, which has no solution in terms of elementary functions.
Nov
11
asked You can't solve Laplace's equation with boundary conditions on isolated points. But why?
Nov
11
comment Curve parameterization trick
This doesn't help you, but I just wanted to see what the curve looked like. i.stack.imgur.com/HDr63.png
Nov
10
comment Differential equation: the law of natural growth and the law of natural decay
The relative decay rate given by (1) is positive. The value of $k$ in equation (2) is negative. This isn't a contradiction because $k$ isn't actually the relative decay rate! You may find it instructive to start from equation (2) and attempt to find the value of (1), that is, $-\frac{1}{m}\frac{dm}{dt}$.
Nov
9
comment Is the optimization problem right?
Perhaps you are asking the following: Consider the problem $\min_{x\in X}\big(a(x)+c(x)\big)$, given that $a(x)=\min_{y\in Y} b(x,y)$. Is this equivalent to solving $\min_{x\in X,y\in Y}\big(b(x,y)+c(x)\big)$? Yes, I believe so.
Nov
9
comment Why aren't numerical methods sufficient to show existence and uniqueness?
Consider the ordinary differential equation $x'=x^2$ with $x(0)=1$. Using any explicit integration scheme, you can obtain a numerical solution extending arbitrarily far forward in time. But the analytical solution is $x(t)=1/(1-t)$, and does not exist for $t>1$.
Nov
8
reviewed Leave Open Is Riemann Hypothesis provable?
Nov
8
comment Why is the nuclear norm called so?
@Mariano: Ah, so it's a 20th-century development, which explains why it isn't in Earliest Known Uses. I should have thought to check Encyclopedia of Math, which does mention the connection straight away. Is it common in mathematics to use nucleus as a synonym for kernel, or to describe things related to kernels as nuclear?
Nov
8
asked Why is the nuclear norm called so?
Nov
8
comment Prove multiplication of column matrix and skew symmetric matrix is null matrix
The step you didn't get uses the fact that $(AB)^T=B^TA^T$, not $A^TB^T$.
Nov
7
awarded  Revival
Nov
6
comment Focus of a parabola, without derivatives
The direction of reflected rays is determined by the normal of the surface. How do you define the normal of a function's graph without using derivatives?
Nov
6
revised How to read mathematical formulas?
"impossible to *read* mathematics" and other edits
Nov
5
comment How special is your random shuffle?
So, I guess the question is mainly, how many shuffles have ever taken place in the world? A Fermi problem, I suppose.
Nov
4
comment On the Name of the Amplituhedron
Presumably it was named in the tradition of the permutohedron, the associahedron, the cyclohedron, ...
Nov
4
revised Optimal Resolvable Steiner Quintuple System covering with circles and ellipses
changed verbatim TeX to rendered TeX
Nov
4
comment Stationary points and gradient?
Yes, WolframAlpha is wrong. Someone tell @in_wolframAlpha_we_trust the bad news...