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Data Scientist @ Explorer Media


2d
comment How can one find intermediate digits of a root of an algebraic equation?
@YvesDaoust that's the beautify of it. using the equation itself as information we deduce more and more continued fraction digits of our number. see Enrico Bombieri's continued fractions and algebraic numbers. our number is definitely algebric, e.g. let $x = z^{12345 \times 3456}$.
2d
comment How can one find intermediate digits of a root of an algebraic equation?
@YvesDaoust I think continued fractions might be more appropriate, given his equation and their good approximation properties.
Jan
21
comment Automorphism group of a lattice's Voronoi cell
It's hard to say since finite subgroups of $O(n)$ can be quite varied. en.wikipedia.org/wiki/Crystallographic_restriction_theorem
Jan
21
comment Automorphism group of a lattice's Voronoi cell
mathoverflow.net/questions/37136/…
Jan
6
comment “Novel” proofs of “old” calculus theorems
math.SE has a faq tag: math.stackexchange.com/questions/tagged/faq+calculus
Jan
6
comment Special functions as representations of Lie Groups
en.wikipedia.org/wiki/…
Dec
31
comment the measurability of $\int_0^t X(s)ds$
Filtration here means $s< t$ implies $\mathcal{F}_s \subset \mathcal{F}_t$. Adapted means $X(t)$ is $\mathcal{F}_t$-measurable. I am trying to think of adapted processes that are not simple...
Dec
29
comment asymptotic expansion for Bessel function $I_0(z)$ in terms of Gauss hypergeometric functions ${}_2F_1$
@Qmechanic don't mind me. Peter showed me his paper in the summer. I have been treating it as a crash course in special functions.
Dec
4
comment What is a concrete example to demonstrate that $\mathcal{O}_{\mathbb{Q}(\sqrt{-19})}$ is NOT a norm-Euclidean domain?
math.stackexchange.com/questions/23844/…
Dec
4
comment Nice proof that $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain wrt absolute norm map
A modern device for quadratic forms is the topograph as discussed by Ch 2 of Topology of Numbers by Allen Hatcher
Dec
4
comment Nice proof that $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain wrt absolute norm map
It's common to talk about $|x^2 - 6y^2 |< 1$ as a sphere even though the interior of a hyperbola. One could solve Pell's equation $x^2 - 6y^2 = 1$ by finding the continued fraction expansion of $\sqrt{6}$, which is periodic. Maybe we can use continued fractions to solve $|(x-a)^2-6(y-b)^2 |< 1$.
Dec
4
comment How to arrange 3 rectangles in a big rectangle
I don't understand $40^2 + 40^2 + 10^2 = 3300 < 10000 = 100^ 2$, so it's not possible to giver the big rectangle with three smaller rectangles.
Dec
4
comment Nice proof that $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain wrt absolute norm map
some ideas maybe here: math.uconn.edu/~kconrad/blurbs/ringtheory/euclideanrk.pdf
Dec
4
comment A specific kind of probabilistic proof for central binomial coefficients
@StevenTaschuk more dangerously, proof of CLT is usually built on estimates of binomial coefficients
Dec
4
comment Prove that the diagonal $∆$ in $S^2×S^2$ is not globally definable by $2$ independent function.
what does globally definable mean?
Nov
30
comment Nobody told me that self teaching could be so damaging…
It's no coincidence I pick Freeman Dyson and Ramanujan since they occasionally worked on the same subject. In addition to QED, Dyson also worked in number theory en.wikipedia.org/wiki/Ramanujan%27s_congruences
Nov
27
comment area of figure in sector of intersecting circles
I was hoping we can use Descartes Circle Theorem. We can identify 4 circles: * the circle $O_A$ with center at $A$ * circle with diameter $\overline{AP}$ * circle with diameter $\overline{PB}$ * unknown circle Unfortunately, these 4 circles are not mutually tangent since the circle with diameter $\overline{AP}$ is not tangent to the circle $O_A$ with center at $A$.
Nov
19
comment The radius of image of a circle under mobius transformation
math.stackexchange.com/questions/360954/…
Nov
18
comment The radius of image of a circle under mobius transformation
I need a way to find the Euclidean center of that circle
Nov
17
comment If $T^m$ is ergodic, so is $T^{m^2}$?
can you say $(T^{m^2}) = (T^m)^m$ ?