Teaching and Applying Möbius Geometry

Zbyněk Šír
Charles University, Prague

In this talk we discuss selected aspects of teaching Möbius geometry to undergraduate students and illustrate how its basic concepts can be applied to a range of geometric problems. Particular emphasis is placed on its connections with projective, differential, and non-Euclidean geometry, as well as with conformal transformations and the theory of holomorphic functions. We also highlight its role in classical results such as the Riemann mapping theorem and discuss geometric applications related to minimal surfaces and isothermal parametrizations.