Geodesic, Geodesical

[Fr. géodesique. See SUPRA.] Pertaining to geodesy; geodetic. Geodesic line. (Geom.) A curve traced on a surface, so that its osculating plane at every point contains the normal to the surface at that point. A geodesic may also be defined as the curve which a string, lying on the surface, would a ume if subjected to tension at its extremities. From this definition it follows that a G. must, under ordinary circumstances, be the shortest line that can be drawn on the surface between any two of its points. The geodesics on a sphere are its great circles; the geodesics on a developable surface become, of course, right lines when the surface is unfolded into a plane.