Euclidean and Other Geometries

Abstract

Geometry has been my favorite subject for years. My topic, Euclidean and other geometries, has been selected to enable me to consider Euclidean geometry as one of several geometries. Such an approach at the secondary school level makes it possible to illustrate the need for the postulates used for Euclidean geometry. This approach also helps the teacher present any given geometry as a particular mathematical system. Especially when properties of several geometries are considered with reference to various models for the geometries, students recognize that postulates are assumptions rather than “self-evident truths.”