Reputation
23,496
Next tag badge:
88/100 score
19/20 answers
Badges
3 38 88
Impact
~463k people reached

Jul
21
comment If the Chaos Game result is a Sierpinski attractor when the random seed is a sequence (Möbius function), does it imply that the sequence is random?
@Noah: For any point $p$ in the Sierpinski triangle there is an infinite sequence $s\in3^\omega$ such that the iterations under that sequence converge to $p$. A length-$n$ prefix of $s$, call it $s(n)$, will take any point in the convex hull of the Sierpinski triangle to within $O(2^{-n})$ of $p$. If for every $p$ and every $n$ the corresponding $s(n)$ appears in the sequence, then every point in the Sierpinski triangle is approached arbitrarily closely.
Jul
21
comment Formal definition of mesh.
A simplicial complex?
Jul
21
comment If the Chaos Game result is a Sierpinski attractor when the random seed is a sequence (Möbius function), does it imply that the sequence is random?
So your sequence is 123123123123... Does the finite sequence 11 appear in it anywhere?
Jul
21
comment If the Chaos Game result is a Sierpinski attractor when the random seed is a sequence (Möbius function), does it imply that the sequence is random?
You also have to ask yourself what it means for a particular sequence to be "random". The matter is quite subtle, and the analogous question for numbers is meaningless: Is 9 random? Is 4?
Jul
21
comment If the Chaos Game result is a Sierpinski attractor when the random seed is a sequence (Möbius function), does it imply that the sequence is random?
Your procedure is equivalent to rolling a three-sided die and moving closer to the 1st, 2nd, or 3rd vertex accordingly. The Sierpinski attractor will appear if every finite sequence of 1s, 2s, and 3s eventually appears in the sequence. This does not necessarily mean that the sequence is random; for example, it could be the sequence 123111213212223313233111112113..., i.e. (1)(2)(3)(11)(12)(13)(21)(22)(23)(31)(32)(33)(111)(112)(113)...
Jul
20
comment Is Levenshtein distance transitive?
@Brian: Yes, all edit distances with symmetric non-negative costs are metrics. Brett: I think the concept you're looking for is that of a metric space.
Jul
20
revised Derive Cartesian cubic Möbius strip from parametric
deleted 4 characters in body; edited title
Jul
20
comment Find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$.
Thank you. ${}$
Jul
20
comment Find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$.
My comment is still a counterexample to the updated answer.
Jul
20
comment Find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$.
"Among $A,B,C$, the closest point to $Q$ is $C$ and the second closest point is $B$. This gives that the solution is somewhere on the $BC$ edge" This is not true in general. Consider the triangle with vertices $A=(-10,0,0)$, $B=(10,0,0)$, $C=(0,1,0)$ and the point $Q=(1,-1,0)$.
Jul
20
comment How can I use Banach Contraction Principle to solve $Ax = b$?
Didn't Ittay Weiss answer your question half an hour before you asked this one?
Jul
19
comment Why the length of the zigzag curve approximating the circle does not approach the length of the circle?
Let $F_n(x)=\frac1n\sin(nx)$. Then clearly $F_n(x)\to0$ but $F_n'(x)=\cos(nx)\not\to0$.
Jul
17
comment Verify that $\binom{n+1}{4} = \frac{\left(\substack{\binom{n}{2}\\{\displaystyle2}}\right)}{3}$ for $n \geq 4$
Hints: (1) How are two pairs of two things like one quadruple of things? (2) What if both pairs contain a common element? These are two independent hints.
Jul
17
comment Verify that $\binom{n+1}{4} = \frac{\left(\substack{\binom{n}{2}\\{\displaystyle2}}\right)}{3}$ for $n \geq 4$
Please don't use display math in titles; it takes too much vertical space on the front page.
Jul
17
revised Verify that $\binom{n+1}{4} = \frac{\left(\substack{\binom{n}{2}\\{\displaystyle2}}\right)}{3}$ for $n \geq 4$
added 6 characters in body; edited title
Jul
17
comment Is there anything special about a transforming a random variable according to its density/mass function?
You're aware that if $F$ is the cdf of $X$, then $Y=F(X)$ is a uniform random variable between $0$ and $1$?
Jul
17
comment Is the constraint $A^2 = B^2$ convex
Your last sentence is not technically true (consider $\lfloor x^2+y^2\rfloor=0$), but it's true enough for practical purposes. :)
Jul
16
comment Reconciling two intuitions about convolution
@Cameron: Do you think an natural explanation might have to do with the fact that convolution is a sum of translations, and the Fourier modes are precisely the eigenfunctions of any translation operator?
Jul
15
comment Can I have a logical explanation for why this number is so ridiculously close to a whole number?
Why do you think the answers to the other question are not trying to give "logical reasons"?
Jul
14
comment What is the area of the shape defined by the locus of a point on a circle rolling around another circle?
The shape is an epicycloid, more specifically a cardioid, and its area is given in the Wikipedia article. How to compute the area of a parametric curve is also on Wikipedia.