 ![The geodesic on the Mobius strip shown on the left on a single copy of the space. We see that the line is discontinuous under the identification and has a sharp corner at the join. On the right is the same line but represented in a double cover of the space where we have used the diad $\mathbf{e}_0$ on the left and $\mathbf{e}_0$ on the right, swapping the orientation between copies of the space. With this choice we recover what we would expect a geodesic to look like on the double cover with metric given in terms of $x$ and $Y$.[]{data-label="GeoMobius"}](GeoMobius