Geodesics are paths in spacetimes that have ``extremal distance'' They can be thought of intuitively as the ``straightest possible paths'' in curved spacetime Physically, geodesics are trajectories of particles in free-fall (no forces acting on the particles)
On a Riemannian manifold or some other metric space, a curve which is the shortest path between any two points on it that are sufficiently close together
(mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere)
A circular line that goes around the full width of a sphere (like the equator or any of the longitude lines that go all the way around the earth) Geodesic domes get their name because in most of these domes, the edges lie on geodesic lines Geodesics are also called "great circles" because they are the largest circles you can draw on a sphere