Introduction to Complex Geometry
Instructor: To be announced
Coaches: 郝泽平,王怀澈
Course description: This course explores the rich interplay between complex numbers and classical Euclidean geometry. We begin by introducing complex numbers as points in the plane, where their algebraic operations naturally translate into geometric actions. This perspective provides powerful tools for analyzing geometric transformations, solving construction problems, and proving elegant theorems with striking simplicity.
We will examine how complex arithmetic encodes rotations, reflections, dilations, and inversions, and how these operations can be used to illuminate classical geometric results — including triangle centers, circle configurations, Möbius transformations, and the geometry of the unit circle. If time permits, we will also touch on the geometry of elliptic curves. No prior knowledge of complex analysis is required; we will develop all necessary foundations in class. The course is ideal for students with a solid background in Euclidean geometry and an interest in applying algebraic techniques to geometric reasoning.