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I have known the data of $\\pi_m(so(n))$ from this table I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof To gain full voting privileges,

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Welcome to the language barrier between physicists and mathematicians How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

I'm not aware of another natural geometric object.

What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ The answer usually given is A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg Later he goes back to his place and finds out that this whole 'age' reversed process occurs 6 times

And if they (mom + son) were lucky it would happen again in future for two more times. You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do i get it

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Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter Assuming that they look for the treasure in pairs that are randomly chosen from the 80 The son lived exactly half as long as his father is i think unambiguous Almost nothing is known about diophantus' life, and there is scholarly dispute about the approximate period in which he lived

There is no reason to think that the problem has a historical basis. The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices