On the Shape of a Curve

Abstract

This chapter discusses the shape of a curve. In particular, the general polynomials are open and dense in the set of all polynomials and their complement is of measure zero. Thus, the special polynomials in their complement are always limits of the generic ones so that even their properties can often be best understood as the limiting property of the generic ones. At this stage, the pure temptation is of course to proceed further and ask the corresponding question for polynomials in more variables and the moment one succumbs to it, one is introduced into the heart not only of topology and algebraic geometry but also of much of modern mathematics.