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7h
comment Law of sines: uniform proof of Euclidean, spherical & hyperbolic cases
(Tangentially) related: uniform proof of the fact that 3 altitudes of a triangle are concurrent
2d
comment Definition of bordism - gluing manifolds with structure
Related: math.stackexchange.com/q/410917
Dec
16
comment Reference Request: Thom Spectrum of a virtual vector bundle
AFAIR, 1) For Thom spaces of vector bundles $\operatorname{Th}(\xi+1)=\Sigma\operatorname{Th}(\xi)$. 2) Any virtual bundle is of the form $\xi+n$, where $\xi$ is a vector bundle and $n$ is an integer. 3) For spectra suspension map is invertible.
Dec
15
comment Law of sines: uniform proof of Euclidean, spherical & hyperbolic cases
@Willemien Are you asking if the law of sines (in this form) true in hyperbolic geometry? Certainly — see e.g. en.wikipedia.org/wiki/Law_of_sines#Unified_formulation
Dec
14
comment Ramanujan-type trigonometric identities with cube roots, generalizing $\sqrt[3]{\cos(2\pi/7)}+\sqrt[3]{\cos(4\pi/7)}+\sqrt[3]{\cos(8\pi/7)}$
Thank you. I need to think about it for some time.
Dec
14
comment Fermat's Challenge
See e.g. thm 3.4 @ math.uconn.edu/~kconrad/blurbs/gradnumthy/mordelleqn1.pdf
Dec
13
comment spherical triangle: law of sines
related: math.stackexchange.com/questions/69345/…
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
Oh, you're right, for finite fields the Galois group can't be $S_3$...
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
No, the question doesn't require the polynomial to have a root mod all p=4k+1 — and since 1/3<1/2 I don't see an immediate contradiction with Chebotarev's theorem.
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
Ah, I see. But IMHO the question asks about a cubic polynomial that (like $x^2+1$) doesn't have zeroes mod all primes of the form $4k+3$.
Aug
1
comment Does there exist a cubic polynomial $f(x)$ such that $f(x)\equiv0 \pmod p $ has no integer solutions if $p\equiv 3\pmod 4$?
@gammatester p=3 is not 1 mod 3
Jul
18
comment Intuition for the definition of the Gamma function?
(Somewhat) related: How to come up with the gamma function? & Understanding the Gamma function
Jul
15
comment Sum involving binomial coefficients
Well, have you tried guessing general answer from first few values?
Jul
15
comment How to compute homotopy classes of maps on the 2-torus?
(I wish I knew a reference where all this is explained more clearly...)
Jul
15
comment How to compute homotopy classes of maps on the 2-torus?
@Qiaochu ...i.e. $\pi_2(X)/\langle t-t^a,t-t^b\mid t\in\pi_2\rangle$ is actually $H^2(\mathbb T^2;\pi_2(X))$, where $\pi_2(X)$ is the local system s.t. generators of $\pi_1(\mathbb T)$ act as $t\mapsto t^a$ and $t\mapsto t^b$.
Jul
15
comment How to compute homotopy classes of maps on the 2-torus?
@Qiaochu The answer for $D^2$ is different because the coboundary map is different. For $[S,X]$ (and let's consider the case $\pi_1(X)=0$ for simplicity) we're talking about $H^2(S;\pi_2(X))$.
Jul
15
comment How to find the length of diagonal of a rhombus
(...and now we have answers to two different questions in one place...)
Jul
15
comment How to find the length of diagonal of a rhombus
I don't know why someone decided to overwrite an old question with a different one — rolled back.
Jul
15
comment How to compute homotopy classes of maps on the 2-torus?
@Qiaochu Let's see. In the same spirit for $D^2$ we have 'a' trivial element of $\pi_1$ and an element of $\pi_2$ up to some equivalence relation; and in the part 'Let's see if this element of $\pi_2$ is well-defined' we have $s'=s+t$ — i.e. equivalence relation identifies all elements of $\pi_2$. That's the correct answer.
Jul
12
comment Probability of their's constituting a triangle?
...and see also mathoverflow.net/questions/2014