Mathematical Fallacy - The $17$ camels Problem.
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 get $9 + 6 + 2 = 17$ …
Fundamental group of the special orthogonal group SO(n)
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).
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s. $\\pi_m(SO(N))$
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 …
Prove that the manifold $SO (n)$ is connected
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 ...
Diophantus Epitaph Riddle - Mathematics Stack Exchange
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 $80$, and so …
Dimension of SO (n) and its generators - Mathematics Stack Exchange
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 ...
orthogonal matrices - Irreducible representations of $SO (N ...
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 ...
Distinguishing $SU(n)$ from $SO(n)$ - Mathematics Stack Exchange
May 24, 2017 · Suppose that I have a group $G$ that is either $SU(n)$ (special unitary group) or $SO(n)$ (special orthogonal group) for some $n$ that I don't know. Which "questions ...
lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators. …
Representation theory of $SO (n)$ - Mathematics Stack Exchange
Regarding the downvote: I am really sorry if this answer sounds too harsh, but math.SE is not the correct place to ask this kind of questions which amounts to «please explain the represnetation …