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Jul 29, 2020 · Also $18$ is divisible by each of $2,3,9$; so the $1$ st son gets $9$ camels, the $2$ nd son gets $6$ camels, and the third son gets $2$ camels. Miraculously , we g
Aug 19, 2025 · Diophantus' childhood ended at $14$, he grew a beard at $21$, married at $33$, and had a son at $38$. Diophantus' son died at $42$, when Diophantus himself was $80$
Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned).
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards her
The only way to get the 13/27 answer is to make the unjustified unreasonable assumption that Dave is boy-centric & Tuesday-centric: if he has two sons born on Tue and Sun he will m
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1
Sep 21, 2020 · I'm looking for a reference/proof where I can understand the irreps of $SO(N)$. I'm particularly interested in the case when $N=2M$ is even, and I'm really only ...
Aug 1, 2024 · I was wondering, for the group $SO(n)$, as far as I understand, the $n\\choose 2$ infinitesimal rotations in the plane spanned by $e_i$ and $e_j$ for $0\\le i<j&l