A neighborhood magnification method for solving implicit equations in two variables

摘要

A geometric approach for solving simultaneous equations in the form f(x,y) = 0 and g(x,y) = 0 in two real variables in a given region is suggested. The method, called the neighborhood magnification method, primarily locates a neighborhood of a point of intersection of the graphs of the functions and, by magnification of successively smaller neighborhoods, computes the numerical values of the coordinates of the point of intersection. A simple procedure for generating rough sketches of implicit functions in a given region is also suggested.