Geodesics Using Mathematica

We describe surfaces and geodesics without assuming prior knowledge of differential geometry. This involves selecting and presenting basic definitions and theorems. Included in this discussion are definitions of surface, coordinate patch, curvature, geodesic, etc. This summary closes with a proof of the length-minimizing properties of geodesics. Examples of surfaces of constant gaussian curvature are given and plotted in Mathematica. We also describe geodesics on these surfaces and plot select examples