ABSTRACT
Discussion of non-Euclidean geometry begins with the problems with Euclidean geometry. The parallel postulate and variants of it are examined producing spherical and pseudo-spherical geometries. Curvature is discussed and then the shortest distance between points. This elaborates into differential geometry, geodesics, and metrics. Metrics and metric spaces expand the concept of distance. We then shift to fractals, examining their motivations in nature. We discuss fractals generated by iteration. The concept of fractal dimensions is explored. We return to iteration with an overview of chaos theory.
