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genericname

I was a bit confused by the proof that we need 3 degrees of freedom. So from what I understand, the idea is that if we specify only 2 parameters. We can still specify multiple rotations. But I don't quite understand the argument behind fixing sao paulo. Does that mean we consider an axis that goes through sao paulo and rotate around that? Or does it mean we can still figure out another way to rotate towards where sao paulo originally was?