Understanding Non-Euclidean Geometry

Starting with special geometric structures of complex plane, students will learn symmetry and conformality on complex transformations; the intriguing correspondence between the complex plane and a sphere; and Mobius transformation. Then students would be introduced to a number of amazing properties of Non-Euclidean Geometry from a modern point of view, including hyper-parallelism, non-Euclidean distance, constant curvature, and hyperbolic trigonometry.