MATH 145 PZ -Transformational Geometry

Institution: Pitzer College

Description: This course focuses on geometry from a transformational point of view. Euclidean constructions lay the foundation for understanding Euclidean reflections and circle inversion (or hyperbolic relfection). The isometry group of the Euclidean plane is investigated and used to prove standard theorems in Euclidean geometry. Projective and hyperbolic geoemtry are introuduced in historical context, and Euclidean models analyzed. These models show that Euclidean, projective and hyperbolic geometries are equally consistent , and provide for explicit descriptions of their isometry groups. Non-Euclidean isometry groups are characterized, and a transformational approach is applied to study non-Euclidean geometry.