Yan - Bin Jia Nov 2 , 2017

Geodesics are the curves in a surface that make turns just to stay on the surface and never move sideways. A bug living in the surface and following such a curve would perceive it to be straight. We will begin with a definition of geodesics, then present various method for finding geodesics on surfaces, and later reveal their relationships to shortest paths. The term geodesic comes from the science of geodesy, which is concerned with measurements of the earth’s surface [1, p. 163]. F. W. Bessel (1784–1846) was involved with determining the shape of the earth as an ellipsoid of rotation. C. G. Jacobi (1804–1851) studied the “shortest curves” on an ellipsoid of rotation which he referred to as “geodesic curves”. The term “shortest curves” had earlier been used by Johannes Bernoulli (1667–1748) and Carl-Friedrich Gauss (1777–1855).