Geodesics on Surfaces

This lecture covers the concept of geodesics on surfaces, focusing on the length of curves within a surface and the properties of geodesics. Starting with the definition of a parametric curve, the lecture progresses to discuss the shortest paths between points on a surface, particularly on a sphere. The instructor explains how geodesics are the paths that minimize distances on a surface, using examples like great circles on a sphere. The lecture also delves into the formal definition of geodesics and the role of normal unit vectors in determining geodesic paths. Additionally, the lecture explores the intersection of spheres with planes and provides proofs and evidence to support the concepts discussed.