ABSTRACT
We start exploring topics in geometry. Geometry is the study of shapes such as lines and planes, or, more generally, curves and surfaces, etc. There are two paths towards this study: the synthetic one and the analytic (or algebraic) one. Synthetic geometry is geometry without algebra. Analytic geometry is geometry through algebra. Synthetic geometry originates with the Greek mathematics of antiquity (e.g., the treatise of Euclid). Analytic geometry was invented by Fermat and Descartes. We already encountered the synthetic approach in the discussion of the affine plane and the projective plane which were purely combinatorial objects. Here we introduce some of the most elementary structures of analytic geometry. We start with lines. Later we will look at more complicated curves.
