The shortest path connecting two points in a space;
Geodesics are only locally the shortest distance between points, and are parameterized with "constant velocity". Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points. noting that an elastic band stretched between two points will contract its length, and in so doing will minimize its energy. The resulting shape of the band is a geodesic.'Wikipedia Article
Geodesics can also refer to "two events separated in time, a geodesic is the natural path things would take in space-time to connect one event to the other." (Randall 105)
Cocktail Party BanterOur pilot followed the Geodesic flight pattern perfectly, so we got to Denver thirty minutes earlier than expected.
Literary Context"For example, routes of airplanes that follow great circles on the Earth are Geodesics."(Randall 105)
Randall, Lisa. Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions. New York: Ecco, 2005. Print.