= Metric geodesic
{title2=$d(\gamma(s),\gamma(t))=|s-t|$}
A unit-speed metric geodesic in a <metric space> is an <isometric embedding> $\gamma:I\to X$ of a <real interval>. Every restricted segment realizes the distance between its endpoints. A one-point interval permits a constant segment. In a unit-edge graph, shortest edge paths parametrized by <metric path length> are metric geodesics; no smooth structure is required. This is stronger than the differential definition of a <geodesic> in a <Riemannian manifold>, which need only minimize locally: on a unit circle, an arc of angle $3\pi/2$ is a Riemannian geodesic but its endpoint distance is only $\pi/2$.
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