Plane Curves and Space Curves

Abstract

If we draw the graph of a function y = f (x) on the plane, we obtain a curve. For example, the graph of y = x² is a parabola. Similarly, the graph of a function x = g(y), for example x = y², is also a curve. Both y = f (x) and x = g(y) have one of the variables as an independent variable, and the other as a dependent variable. So x and y are not equally treated. If we rewrite these in the form y – f (x) = 0 or x –g(y) = 0, we can unify them in the form.