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- Jun 20, 2014

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Consider the open unit disk $\Bbb D\subset \Bbb C$ with Riemannian metric $ds^2 = \dfrac{\lvert dz\rvert^2}{(1 - \lvert z\rvert^2)^2}$. Find a formula for the (Riemannian) distance between two points in $\Bbb D$, and use it to find the distance between $-\frac{1}{2}e^{i\pi/4}$ and $\frac{1}{2}e^{i\pi/4}$.

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