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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?
Jul
6
comment Edited: Implicit Differentiation of Life-History Function
Mathematica gives me $\dfrac{\mathrm d\lambda}{\mathrm d\alpha} = \dfrac{(s-\lambda )^2}{s-\exp[-(\alpha +s/(\lambda -s))^{-1}] (\alpha (\lambda - s)+s)^2}$.
Jul
6
comment Why does $\sum a_i \exp(b_i)$ always have root?
I think the title should say "Why does ... always have a root?"
Jul
5
comment Guessing the length of a playlist on “shuffle random?”
I suppose the distribution of repeats, i.e. how many songs were heard twice, how many were heard thrice, and so on, does not give any additional information?
Jul
3
comment Why is not parity transformation just a rotation?
For any vector $v\in\mathbb R^3$ there is some rotation that maps it to $-v$, but there is no one rotation that maps every vector $v$ to $-v$. For example, rotating by $180^\circ$ about the $x$-axis maps $(0,0,1)$ to $(0,0,-1)$ but does not map $(1,0,0)$ to $(-1,0,0)$.