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If I define the two dimensional sphere in the usual way, this gives me a metric ##ds^2 = r^2 d\theta^2 + r^2 \sin^2 \theta d\phi^2##. Can I just define a new coordinate system giving a point coordinates ##(\theta', \phi') = (\theta r^2, \phi r^2 \sin^2 \theta)##?. This gives me the metric ##ds^2 = d\theta'^2 + d\phi'^2##.