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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.
Jul
12
comment How do you call a 3d convex shape made of 8 arbitrary points?
A polytope in 3D is called a polyhedron, just like a polytope in 2D is a polygon. If your polyhedron is so much like a box that it has six quadrilateral faces, it would be a hexahedron.
Jul
12
comment 3D Shape with only coplanar faces?
Sorry, that was a misleading image. I meant this. No interior connectors.
Jul
12
comment 3D Shape with only coplanar faces?
For a nontrivial example, interpret the small stellated dodecahedron as having $60$ triangular faces instead of $12$ pentagrammic faces.
Jul
12
comment 3D Shape with only coplanar faces?
Like this shape with $54$ square faces? :)
Jul
12
comment When is the inverse of a reciprocated function equal to the function?
I would interpret "inverse of a reciprocated function" to mean $g^{-1}$ where $g(x)=1/f(x)$.
Jul
12
comment What kinds of functions have fixed points?
I think you mean Brouwer's fixed point theorem, not "Brewer's"?
Jul
12
comment What kinds of functions have fixed points?
Nitpicks: Not all cubics start positive and end negative. Also, not all odd-degree polynomials have at least one fixed point, because a polynomial of degree 1 is an odd-degree polynomial. Anyway, I don't think anything more can be said beyond Mihir's comment.
Jul
11
comment Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)
Yes, you've got it.
Jul
11
comment Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)
Pick a line segment $AB$ in the plane. Construct an equilateral triangle one of whose edges is $AB$. Now construct a square. Then a hexagon. Then a dodecagon. Imagine what a 100-gon on $AB$ would look like. Can you see a pattern?
Jul
11
revised Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)
use non-mobile Wikipedia links
Jul
10
comment Sphere intersecting a triangle
I think what the author is saying is that if the sphere collides with the inside of the triangle, then any collison with a vertex or an edge must happen later (if at all). It's very confusingly written, but this is the only interpretation that's correct and consistent with the later text.
Jul
9
comment Is Tolkien's Middle Earth flat?
It minimizes $\max|d'_{ij}-d_{ij}|$. I should have said "the corresponding flat configuration" related to the assertion in my previous sentence.
Jul
9
comment Is Tolkien's Middle Earth flat?
Since @joriki brought up the accuracy of the distances, I thought I'd check how sensitive the problem is to rounding. Could the apparent non-flatness be a result of someone getting a ones'-place digit wrong? The answer is no: at least one of the distances has to change by at least $26.3$ miles. The "nearest" flat configuration has distances $839.3$, $761.3$, $806.3$, $1138.3$, $933.7$, and $1471.7$ miles.
Jul
7
comment How to find the shift that minimizes the difference between two vectors?
I think this answer is missing a lot of details. What do you take the derivative with respect to? How do you calculate a "certainty measure"? What does the weighted mean give you?
Jul
7
comment Animation of Weierstrass $\wp$-function as a map from a torus to the sphere?
John Baez talked about it a bit in Week 229 of his This Week's Finds blog. There isn't an animation, but there is a world map that visualizes the function.
Jul
6
comment Algorithm to find shortest path to net values across nodes
I think this is essentially a transportation problem, isn't it?