The golden number and the extraction of edges: application to trace an implicit function

To trace an explicit function, many items of software (for example: Matlab, Mathcad, Mathematica, Gnuplot, ..., under MS-DOS, UNIX, Windows) have been made. The method in theory is simple: if the value of the argument x is given, then we can calculate the value of the function y, as an expression of the given function. To trace an implicit function, there is not at present any efficient method because it raises many problems for the mathematics and computer. In this article, a method concerning the golden number theory is proposed, in order to obtain very quickly the zero points of the implicit function in its definition's domain. The result is ideal; a second or less is needed; the method concerns the extraction and suivie of edges to trace an implicit function.