Geometry in today's world : Euclidean and beyond

The Euclidean approach to the study of the world was very limiting. But since the discovery of the New World, man has developed many new ideas and forms of geometry which have been very useful. For the teacher of geometry, it is important to know the various geometries beyond Euclidean geometry. Therefore, the purpose of this project is threefold: 1) historical, 2) didactic, and 3) practical. First, a short history of modern geometry is presented to show what geometries beyond Euclidean have been developed in the past three hundred years. Secondly, the basic concepts of modern geometry are explained, both non-Euclidean and Euclidean with its new approaches. To help the teacher see the differences between the various approaches to geometry, the new concepts of geometry are applied to several familiar Euclidean theorems. (See more in text.)