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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 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 Diophantus died four years later when he was $84$ Checks out!
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)
Mathematical Fallacy - The $17$ camels Problem. So the Problem goes like this :- An old man had $17$ camels He had $3$ sons and the man had decided to give each son a property with his camels Unfortunately however, the man dies, and in his l
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 matter) What I mean is: It is clear that (in case he has a son) his son is born on some day of the week