geodesic

On a differentiable manifold, specifically one where you can measure distance, i.e. a Riemannian manifold, a geodesic is the (locally) shortest path between two points. Here, locally means that any perturbation to the path makes a longer path (see variational calculus). Imagine two points on a circle. You can go the "short" way or the "long" way. Both are geodesics.