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visits member for 3 years, 9 months
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22h
comment Homology Whitehead theorem for non simply connected spaces
(tangentially) related: Two CW complexes with isomorphic homotopy groups and homology, yet not homotopy equivalent
Apr
13
comment Complex number with 3 dimensions
@BenMillwood The link answers the OP's question «Why is there no complex number in 3 dimensions?» [and what it means exactly].
Apr
12
comment Complex number with 3 dimensions
related: Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
Mar
18
comment closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+…+\binom{n}{n}$
Related: How do I count the subsets of a set whose number of elements is divisible by 3? 4?
Mar
4
comment Show that $\displaystyle\sum_{k=0}^n\binom{2n}{2k}^{\!2}-\sum_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
Related: math.stackexchange.com/q/497470
Feb
12
comment Prove that $x^3 + y^3 = z^3$ has no integer solutions as simply as possible
I've always appreciated that (unlike on many internet forums) on Math.SE answers actually try to answer the question (as opposed to, say, amusing the audience). This one is obviously an exception...
Feb
7
comment Show that ${n\choose r}2^r 3^{n-r}=\sum_{k=r}^{n} {n \choose k} {k \choose r}2^k$
$(2t+3)^n=(2t+2+1)^n$.
Feb
2
comment How prove this $\sum_{k=0}^n \binom{n}{k} \binom{(p-1)n}{k} \binom{pn+k}{k} = \binom{pn}{n}^2 $
(I wonder if there is a binomial identity, generalizing both this one and Dixon's...)
Feb
2
comment How prove this $\sum_{k=0}^n \binom{n}{k} \binom{(p-1)n}{k} \binom{pn+k}{k} = \binom{pn}{n}^2 $
$$ \sum(-1)^k\binom nk\binom mk\binom{-(n+m+1)}k $$ surely reminds of Dixon's identity...
Jan
25
comment Proving that $\left(\frac{\pi}{2}\right)^{2}=1+\sum_{k=1}^{\infty}\frac{(2k-1)\zeta(2k)}{2^{2k-1}}$.
None of downvotes are mine, but how exactly 'this series admits this integral representation — prove it yourself' is any better than 'this series is equal to $\pi^2/4-1$ — prove it yourself'? Maybe experts can see what you're alluding too, but this answer hasn't taught me anything, I'm afraid (and, AFAICS, other users haven't found this helpful either).
Jan
23
comment $1 + 1 + 1 +\cdots = -\frac{1}{2}$
Related: math.stackexchange.com/q/39802 (and links there)
Jan
23
comment Is there a connected topology space that is disconnected by remove any point?
Related: math.stackexchange.com/q/634787
Jan
23
comment How do I see that $x^5+x-1=(x^2-x+1)(x^3+x^2-1)$
$x^2(x+1)A-A=(x^3+x-1)A$. What is your question?
Jan
21
comment Double categories
Related: ncatlab.org/nlab/show/double+category
Jan
20
comment What comes after $\cos(\tfrac{2\pi}{7})^{1/3}+\cos(\tfrac{4\pi}{7})^{1/3}+\cos(\tfrac{6\pi}{7})^{1/3}$?
I'm not sure there exists a (good) generalization in this direction — but maybe you'll find another generalization of the second formula of interest
Jan
19
comment Ramanujan-type trigonometric identities with cube roots, generalizing $\sqrt[3]{\cos(2\pi/7)}+\sqrt[3]{\cos(4\pi/7)}+\sqrt[3]{\cos(8\pi/7)}$
(The question is quite long already, but maybe I'll add some thoughts/comments later...)
Jan
19
comment Why does $1+2+3+\dots = {-1\over 12}$?
See also Infinite series are weird blog post
Jan
19
comment Ramanujan-type trigonometric identities with cube roots, generalizing $\sqrt[3]{\cos(2\pi/7)}+\sqrt[3]{\cos(4\pi/7)}+\sqrt[3]{\cos(8\pi/7)}$
(Answers to more informal question just what's going on here? would also be appreciated.)
Jan
19
comment Non-homotopy equivalent spaces with isomorphic fundamental groups
...and math.stackexchange.com/q/401505
Jan
19
comment Non-homotopy equivalent spaces with isomorphic fundamental groups
See also math.stackexchange.com/q/99302 and math.stackexchange.com/q/88943