Luboš Motl
Reputation
6,215
Next privilege 10,000 Rep.
Access moderator tools
 May 24 comment Linear Algebra Question It was a pleasure, @MAxcoder. Thanks for your bounty. ;-) May 24 comment AES Key Scheduler May 24 answered Simple (even toy) examples for uses of Ordinals? May 24 comment Function growth comparison Compare the $n$th root of these two functions. For the left one, it goes to $10/8$ because the difference between $n$, $n-2$, and $n+3$ becomes negligible when taking the roots, and for the right one, it goes to $\log(n)^5$. The latter is ultimately greater than $10/8$, so its $n$th power is also larger. May 24 answered relations between root lattice and weight lattice May 24 revised Finding Lagrange's form of the remainder with $a = \pi/2$ and $n\to\infty$ Dollar signs added around maths, nothing else May 24 suggested approved edit on Finding Lagrange's form of the remainder with $a = \pi/2$ and $n\to\infty$ May 24 revised A question about integral quadratic forms Math put in dollar signs, no other edits May 24 suggested approved edit on A question about integral quadratic forms May 23 comment Generalized “Worm on the rubber band ” problem @Theo, this implicit isomorphism was just an expression of my lack of interest about the identity of the small guy. ;-) @Jean-Pierre, the result looks qualitatively OK for the situations I know - I just didn't know that you could integrate it in general. So I guess that for general functions $a,b$ it's wrong. Which $a,b$ are you substituting to the result if $a,b$ are whole functions of time? I don't really understand what you mean in that case. May 23 comment Subtract gravity from 3D object in different orientations Dear Steven, a detail, a typo: the operation is called "subtraction", not "substraction". ;-) Unfortunately, I don't understand what the question wants to say unless your desire is to subtract one 3-vector from another 3-vector. May 23 answered Intersecting a polygon with four points May 22 answered Laurent Series and annular regions May 22 comment The graph of $x^{n}+y^{n}=r^{n}$ for sufficiently large $n$ In other words, for large even $n$, $x^n+y^n=1$ is essentially equivalent to $x\approx \pm 1$ or $y\approx \pm 1$ (with the other variable allowed to be essentially anything), which are the equations of the square. Note that neither $x$ nor $y$ can exceed one, so that's why you only get the 4 line segments. May 22 comment The graph of $x^{n}+y^{n}=r^{n}$ for sufficiently large $n$ Let me say an answer using basic maths. Without a loss of generality, assume $r=1$; a different value of $r$ simply scales the picture. More importantly, If $n$ is very large and $x$ or $y$ are smaller than one, then $x^n$ and $y^n$ are much smaller than one - they're virtually zero, unless $x$ or $y$ are extremely close to one. For example, $0.9^{100}$ is still close to zero. So if $x^n+y^n=1$, then either $x$ or $y$ or both have to be extremely close to 1 from below so that the high power contributes almost one. May 21 answered Generalized “Worm on the rubber band ” problem May 21 answered Binomial formula in $GF(2^m)$ May 21 answered Of two variables, which affects 'y' more? May 21 revised Complex Exponential Expansion added 16 characters in body May 20 answered What are the finite subgroups of $SU_2(C)$?