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 $9 + 6 + 2 = 17$ …
Boy Born on a Tuesday - is it just a language trick?
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 mention Tue; if he …
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 ...
The Tuesday Birthday Problem - Mathematics Stack Exchange
In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement does …
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 …
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. …
Find Bayesian Nash Equilibria - Mathematics Stack Exchange
Apr 28, 2016 · The father then randomly handed each son one of the two envelopes with a probability of $0.5$. After both sons opened their envelopes, his father privately asked each son whether he …
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).
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 ...