UWEC CERCA 2025

Fractional Linear Transformations, also known as Mōbius Transformations, play a fundamental role in complex analysis and have significant applications in geometry, physics, and engineering. This presentation explores the mathematical structure of these transformations, defined as functions of the form f(z) = (cz+d)/(az+b), where a, b, c, and d are complex numbers satisfying ad – bc ≠ 0. We will examine their geometric properties, including how they map lines and circles to other lines and circles, and their role in conformal mappings. Additionally, we will discuss applications in computer graphics, control theory, and relativity. Through visual demonstrations and problem-solving exercises, this presentation aims to provide an intuitive understanding of Fractional Linear Transformations and their relevance in various fields.