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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
revised Number of samples needed to get a given expected distance
deleted 325 characters in body
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
answered Number of samples needed to get a given expected distance
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
15
revised proving $\mathrm e <3$
deleted 4 characters in body
Dec
14
awarded  Self-Learner
Dec
14
answered How can I recursively approximate a moving average and standard deviation?
Dec
14
reviewed Approve Why multiplying or dividing a positive value by a negative value gives a negative answer?
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.
Dec
4
comment Animation/deformation among developable surfaces
Sorry, what's the question?
Dec
4
comment How to convert a right angled triangle into a equilateral triangle?
The second picture looks close to equilateral to me. Just move the top triangle down a bit. More precisely, change $o_y$ from $0.5$ to $\sqrt3/4 \approx 0.433$.
Dec
4
comment How do we define interior and exterior of a geometric figure?
@HDE: Yep, What makes the inside of a shape the inside?
Dec
3
revised Distribution of difference of points in same tail of normal curve?
added 395 characters in body
Dec
3
comment If the difference of two i.i.d. random variables is normal, must the variables themselves be normal?
I'm gratified to learn that this is a nontrivial result and I wasn't missing something obvious!
Dec
3
comment Why is a Hyperplane called a “Hyper”plane?
It is called a hyperplane because it is a higher-dimensional generalization of a plane, a two-dimensional subspace in the dimensions. See also hypercube, hypersphere, hyperoctant, etc.
Dec
3
accepted If the difference of two i.i.d. random variables is normal, must the variables themselves be normal?