Introduction and Motivation

In this first chapter, we informally introduce the notion of rational algebraic curves, and we motivate their use by means of some examples of applications. These examples cover the intersection of curves in Section 1.1, the generation of points on curves in Section 1.2, the solution of Diophantine equations in Section 1.3, the solution of certain differential equations in Section 1.4, and applications in computer aided geometric design in Section 1.5.