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1d
comment 3D coordinates of circle center given three point on the circle.
@Behaviour I don't think this is an exact duplicate because the answers to the previous question only work in 2D.
2d
comment Distance between the nail and the center of the disk
I think you mean "in order to find $d$ given $l$ and $r$".
Dec
18
comment Does there exist a 4D torus with a spherical cross-section, analogous to a circle for the 3D case?
+1. Regarding your final paragraph, it might help the OP to first visualize the two-dimensional torus as a "circular shell" in 2D, i.e. an annulus, whose boundary circles have been glued together (after lifting them up out of the plane into 3D).
Dec
18
comment What is connexity (in simple language)?
"Connexity" appears to be a shopping/marketing website. Did you mean connectivity, convexity, or something else?
Dec
17
comment How do you keep track of what vectors nabla ($\nabla$) should be working in on?
I've never seen $\overleftarrow{\nabla}$ before so maybe I don't understand what's going on. I'll just leave this here: Wikipedia's list of vector calculus identities. Apparently $$\nabla\times(A\times B) = A(\nabla\cdot B)-B(\nabla\cdot A)+(B\cdot\nabla)A-(A\cdot\nabla)B.$$
Dec
17
comment what is the most attractive font to use in a mathematical document?
The question in the title is completely subjective. The question in the body, if interpreted as "How can one make a Word document with mathematical equations be typographically similar to a document produced with TeX?", is reasonable, and the title should be changed to match it.
Dec
17
comment Arc length and curvature for logistic curves
What have you tried so far?
Dec
17
comment What distribution would describe this?
@GenericNickname: Yes, but linearity of expectation holds for dependent random variables too. Henry is computing the expectation of the sum of random variables $X_i = \{\text{$1$ if basket $i$ is good, $0$ otherwise}\}$.
Dec
17
comment A question in paper “Fitting helices to data by total least squares” writen by Yves Nievergelt in 1996
It looks like your $S$ is the paper's $-S$. That's fine, because in general singular vectors are only determined up to sign: if $A = U\Sigma V^T$ is a singular value decomposition, so is $(-U)\Sigma(-V)^T$.
Dec
16
comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
By the way, this is a specific case of neuguy's example of distance on a graph, in this case a star graph with three leaves.
Dec
16
comment Is there an error in my matrix proofs (Also: potato quality jpeg errors present)
I prefer to think of it like, $A^3=AAA$ so $(A^3)^T=(AAA)^T=A^TA^TA^T=AAA=A^3$.
Dec
15
comment Is indefinite integration non-linear?
@Henning, vadim123: Ah, so you actually just define $0[x]$ to be $[0]$. It would be helpful to add those definitions to the answer, because a naive interpretation of the notation (as in my previous comment) can lead to errors.
Dec
15
comment Is indefinite integration non-linear?
I want to like this answer, but I don't see how $0[x]=[0]$. Zero times any function in $[0]$ is identically zero, so the result collapses to the singleton $\{0\}$, not $\{C:C\in\mathbb R\}$.
Dec
15
comment From the viewpoint of modern geometry, is there a “best” definition of the term “triangle”?
I don't know what the best definition of a triangle is, but the definition of a $2$-simplex is the convex hull of $3$ affinely independent points.
Dec
15
comment Number of samples needed to get a given expected distance
That's a good question. I think what I meant was "when $F(r)$ approaches $1$ rapidly enough that large values of $r$ (relative to the curvature of the surface) can be neglected". This will depend on $n$, $A$, and the curvature of the surface, but I haven't worked out the details.
Dec
15
comment Number of samples needed to get a given expected distance
You'll have to assume that $d$ is sufficiently smaller than the "feature size" of the surface. Otherwise, if the surface is long and skinny, like say a cylinder with radius $r \ll d$, it will behave like a one-dimensional domain instead.
Dec
15
comment proving $\mathrm e <3$
@Approaching: There, I fixed it.
Dec
6
comment Slice an ellipsoid into equally thick slices for maximal surface
A neat question and an unexpected (to me) answer. +1's to both of you!
Dec
4
comment What does “adic” mean?
I always assumed, like user8268, that it was by analogy with dyadic, triadic, tetradic, etc. Make the root number a variable, $p$, and there you go.
Dec
4
comment Let $S$ be the surface generated by the circles of radius $b$, find a parametric expression for $S$
Are you sure the normal to the plane is $(y',-x',0)$? If the plane of the circle is orthogonal to the curve, then its normal should be parallel to the tangent $(x',y',0)$, and $(y',-x',0)$ would be a vector along the plane of the circle.